Try fitting a heat shield under the master cylinder and reservoir.

Have you tried bleeding the brakes or changing the fluid? It may have water
vapor in it.

Besides the fluid, as others have mentioned, it could be the valve in the
booster leaking as though the brakes were applied. Disconnecting and
plugging the vacuum line for a test (warning - the brakes will be too stiff
to drive safely that way) with the engine hot will tell the difference.
Problem goes away, bad booster or adjustment. Problem stays; bad fluid.

Or you can bleed the brakes until the fluid runs clear and see if that helps
;-)   Couldn't hurt.

BTW, the engine shouldn't show hot on the guage at idle, even under the
worst conditions. If it does, the viscous fan clutch is probably bad. They
are expensive but effective. In Phoenix a new one kept the temperature guage
at center even when the outside temperature was above 110F and the AC was on
high. Before I replaced it the guage would touch the red in a few minutes
and drop quickly after we got rolling.

Mike