Sounds good in theory, but the actual application could be difficult and may not be beneficial. Off the top of my head, you'd probably want a refrigerant loop, that way you can heat one side and cool the other without having any impact on the lifting ability of the envelope. The only energy expended is in circulating the fluid. The catch of course is this system adds a lot of weight.
A slightly different concept is jet engines like on the X-30
The fuselage is shaped to act as both an intake and exhaust, using the pressure drag of the airframe to compress the air for the intake and generate thrust from the exhaust. Coolant (fuel) circulated through the forward body of the aircraft would increase the compression efficiency (not much), reduce skin temperatures as so not to melt the airframe (a lot), and increase the combustion efficiency of the fuel (a little).