Actually if you examine adiabatic cooling you will note that it is proportional to the pressure drop; so raising the IP actually means just a little LESS cooling.
Nope

For the first stage 25psi would only represent 1% if we talk about an LP tank at full pressure. And the further we suck the tank down the less cooling will occur, yet for the second stage it will constantly be at 16% more at depth and this is where the water would be likely the coolest.