Ok, I know it's only been a few minutes, but the more I think about it, it *should* work.
It might technically "work", but it will completely invalidate the ability of the thermostat to thermo-regulate correctly, will most likely cause damage to the thermostat itself, and will put the animals at risk.
The Earth is the cradle of mankind, but one cannot live in the cradle forever. -Konstantin Tsiolkovsky