H2 generator cooler

Ok, so the more electrolyte you add, the more h2 you produce but also the more heat you produce. . .correct? So if you could have a cooling system for the solution, you could add more electrolyte and produce more h2, but keep the water at a nice happy temperature. . .correct?

Well what if you stuck a thermoelectric cooler on the end of a big stainless steel bolt, stuck the bolt into your generator, and stuck a huge heatsink on the end of the bolt? It should be able to keep it at, well at least a little bit cooler temperature and still produce more H2.

I just don't know if it would screw with the electrolysis process. . .

Whadya think?