I've got an Aeron, and I'm pretty sure that it's a little more expensive than you're looking for.
In Europe it's hard to find good used ones but in the U.S. there are plenty of used Aerons to buy at real bargain prices. These things come with 12 years warranty: I think it's a non-transferrable warranty but the very fact that give a 12 years warranty speaks for the quality of the chair.
For the OP: the model is 20 years old by now but despite trying many other chairs (including much more fancy Herman Miller ones with better back support), I never found any chair, besides the Aeron, in which I never sweat. That's thanks to the "pellicle mesh" present everywhere. Wikipedia says (I know, I know, you can't always trust what Wikipedia says) that "aeron" stands both for "aeronautics" and "aeration". To me the "aeration" part is the most important: I'll never ever be able to work again in a chair in which I'm not sitting on a "pellicle mesh": I hate sweating
So it's "expensive" but compared to a $200 office chair, a used Aeron in the U.S. may not be that expensive.
Now of course YMMV: some people do not like the Aeron (for example some find it uncomfortable because part of their body touches hard part on the Aeron: I honestly have no idea what they're talking nor how their Aeron is setup... I'm --of course-- sitting on mine right now and I feel like I'm "floating" in space).
To each his opinion: bet would be to try one first and be sure you like it.
I sweating is a problem for OP, then there are also other, less expensive (but maybe not less expensive than a use Aeron), office chairs that also have some kind of "mesh" on which you sit.
Note that sitting on a chair for two minutes is not enough to determine if it's a chair in which you're going to sweat from the back / butt or not.
