Is it possible to fully utilise excess heat from an aircraft to power other systems required for the aircraft to function?
There are heat engines that convert heat into mechanical energy, which can drive useful things around the aircraft. Examples that actually drive systems that we use are 


The steam turbine used for electrical power generation in remote area's, driven by the waste heat from gas turbines.
The stirling engine, used for driving submarines due to it being whisper quiet.
The classical steam engine, also very quiet.


All these engines come at a weight penalty of course. It makes a lot of sense to add a steam turbine to a gas turbine in a power station; adding a steam turbine next to the jet engine is less clearly beneficial. It has not been done.

So yes some of the waste heat of the aircraft engines can be used. But thermodynamics says that never all heat can be transformed - the theoretical maximum efficiency is a function of the maximum and minimum temperatures. Only a heat engine with a perfect Carnot cycle, a heatsink of 0 K or an operating temperature of $\infty$ K and no heat loss other than through the engine process will transform all heat. And we cannot make that in an environment that is neither 0K nor $\infty$ K.