I only have one case fan anyway — an exhaust sysfan in the standard old location under top-mounted PSU.
Believe it or not, my GFX cards (3 different ones so far) for some reason tend to glitch even with case wings removed. When I closed the case, I even had a reset-requiring glitch today during normal office work (for the first time in the last 15 years or so) on a card that was hot but still perfectly touchable on all of its accessible surface (perhaps mem chips/controler overheated, Sapphire HD 4850s used to have this problem). But again, with removed case wings I've seen two different ATI HD 4850s and one GF GTX 460 crash or stutter (including driver loss of control and recovery in the Windows Aero interface).
I wonder if my (much hated) mobo isn't faulty or something. Which kinda makes me want to discard the whole thing. Should have upgraded the entire PC minus GFX, PSU and HDD back when the 460 was alive and I had more money.
Re: new case, I kinda I feel I need one. I've just accepted some overtime this week, so I'll have a bit more cash. Is there any specific model I could just buy without having to devise airflow schemes in my own head? I'm not above cutting up a freaking vacuum cleaner hose to make an airduct, but I'm really not good at airflow design with modern computers.
Need: No vibration, for health reasons. Kinda precludes < 120 mm fans. The brushing and whooshing isn't bad, though the quieter the better. Would be great if I could avoid echo effects etc. too.
Prefer: No huge side fan on the side of the case because that's where my legs are (already getting colds from the computer), and I'd rather keep the PC under my desk in the corner of the room, because there's very little place for it otherwise.
With some pain I could probably fork out the cash for an entire new rig, but I had to upgrade a lot of costly software this year and still have some lare and pressing expenses this year or early next year (several thousand euros to wrap up an overdue degree at uni), so I'd rather not. Hence I'm essentially looking at these three basic options:
1. Best bang for the buck in terms of pure feature enablement and FPS relief, for this rig, no thought to the future. Likely meaning getting a used old formerly high-end card (something that was made to cost $700 on release) with emphasis on 2013 or older games, maxed out in 1920*1080.
2. Cheaping out to near max and avoid dumping money in an old rig... and overloading the PSU, killing the airflow or temps or any combination of the foregoing. This likely means just getting something better for like $20–30 more than a used 460 costs.
3. A card that will last me long enough to be the first GFX in my new rig in 2 years or so (without or without buying an additional one for SLI/Crossfire later), which leans heavily towards newest cards from the midrange.
And I kinda really need a new GFX because:
1. The performance of a single HD 4850 is too weak. It already had been in 2012.
2. I actually have two HD 4850s — one is unstable under loads (which is also why Crossfire won't work, as it exacerbates the problem and crashes all the time) but quiet with Accelero S1 and big fan (sometimes unstable when quiet... memory?), the other has twice more more RAM and is stabler but is also a brutal murder on the eyes (even when locked inside this huge 10 kg iron coffin from Chieftec and set on the lowest rotation speed it will accept).
So right now I'm thinking about the following scenarios re: GFX replacement, which are my detailed options, which are way, way too many and make my head hopelessly spin:
1. A 570ti (preferably NIB) not because of GFX power or system power consumption but because of the low TDP (60 W), which should be a more than manageable heat dump with one of those beefier whole-card non-reference coolers from certain manufacturers. If I took a version that had the 6-pin AND a beefy cooler, I would have an to overclocking reserve, too. Alternatively, I could pick a low profile and short version (the size of my X-fi Titanium soundcard) for better airflow inside the case.
2. R270(X) for better performance for the same price.
3. An ATI 7850 or even 7870 LE/XT (Tahiti core) for the same price actually as a GF750ti and a ton more power, but much more heat and power consumption for my physics-challenged brain to worry avoid.
4. GF770 for the ultimate power within my price range and PSU capacity. Not really all that expensive relative to the other cards.
5. GF960 to go light on the energy and wattage (lighter than the 460) but get the newest tech and the longest-lasting potential (I could then buy a new computer a little faster faster, i.e. without having to buy a new GFX card initially).
6. ATI 280X for the same but less energy saving and more robust architecture. Those nVidia mid-range cards are so freaking flimsy. My 7600 GT survived one year and my GTX 460 2.5 years, bought bought NIB.
7. The odd GF 660–680 or 750–760 (or cheaper 7850) essentially for costing just a little more than another GTX 460.
8. GTX... 480, as it can't be worse than a 460 and is cheap enough. But a huge power hug too.
But I'm reluctant to go with a 7850 from ATI or a 750ti or weaker from nVidia because they actually produce fewer FPS in Starcraft 2 (yes, oddly, GTX 460 beats GT 7850 by at least 5 fps, along with many other cards; GTX seems to be very lucky in SC2 for some reason) and possibly in other games. There is a real possibility of some of those cards performing worse than the GTX 460. And I'm also worried whether 7850 will stay cool and stable where a 4850 could not.
At the same time, I'm reluctant to spend a ton of money on a powerful card for a bottlenecked computer.
Hence I'm kinda inclined to grab a Tahiti 7870 XT/LE for <$140 (after converting from PLN), which looks like the best bang for the buck alongside a GTS 770 for $170-185 (same price as the cheapest used R280X sometimes appear with BuyNow) or take the safer course power-and-heat-wise and pick up an R270 (NIB) for the same price.
Re: my cooling/airflow situation:
My desk is in the 'north-west' corner of the room. My computer almost sits in the room corner (separated from the wall by desk legs). It really is awfully cold down there (I get colds all the time, sometimes wrap a blanket around my knees), but the thing still overheats. It also catches a ton of dust very quickly, even with wings removed. The case is a very old 10 kg thick iron box (ice cold in touch almost all the time), a mini/midi tower just a bit taller than a normal-sized mobo + PSU. These days I have a taller desk with also no drawers (writing table basically), so I could accommodate a big tower (+15 or +20 cm case height). My apartment probably had a less than fully reliable power grid, also other devices have power problems and fuses go out every now and then (e.g. when I turn on the laundry machine and the oven and computer and TV at the same time on weekends). It never leads to my PC actually shutting down or something, but I don't trust the power that comes from the wall. Other than all this, perhaps I'm blaming the grid or airflow for mobo damage, can't exclude this. I can't really move my PC from its corner, so I'd rather not have a huge side fan, as it would blow right on my nees.
At this point, I'd be perfectly content to just pay a couple dozen bucks more and quit the overanalysing and wasting your time while and my own where I could just read a book or play a game. I feel like I'll make it up fast with overtime at work than I will arrive at solutions when thinking more at this stage.

… which, however, is what I've just done, there should be some extra bucks to play with. Not enough for a PC, more than enough for a card.
Perhaps I could buy both a case (especially where a cheap one will do and the same vendor can add some fans to the shipment within one shipment fee) and a card.
If a cheap case and a cheap GFX card is your suggestion, then right now I can afford to get both. Just perhaps not $400 total.
If Polish text doesn't scare you and/or if you're feeling bored somewhat,
here's where I'd be buying from. Narrowed down to unused boxes on BuyNow, capped at PLN700. I would prefer to stay under PLN 350, though. Under PLN200 would be sweet.
Cultural flavour: A lot of US brands don't exist in this market. Antec and CoolerMaster does, also Corsair... Modecom is a local brand that's uninspiring but occasionally solid enough for some purposes (definitely better than noname but not as good as established brands). Unfortunately, these all look like very old designs for old PCs. Unfortunately as well, same stuff is going to cost much more in real shops (even those that really mail-order operations), so I'm kinda stuck with the place.
Alternatively I could just start with my old Chieftec with wings and go from there. Don't really need pre-made screw holes for fans, as long as I have a piece of cord and a fan cable long enough.