Can we use the heat to boil water to turn a turbine? Or would the water never cool enough to be used again?
What about using the heat to create pressure and then releasing the pressure to help move the fly wheel?
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What you’ve described is a type of system used in power generation called combined cycle. They use a gas turbine to spin a generator, then they take the exhaust from the turbine and use it to generate steam. The steam drives a turbine, which is also connected to the generator. The steam then goes to condensers, and returns to the steam generator still very hot, but as liquid. These systems run under high pressures to increase efficiency.
We don’t do this in cars because the systems required to support this cycle are very large. As you scale them down, the their efficiency drops. There isn’t any way around that efficiency drop, because it’s down to some fundamental geometry and physics.
For example, the volume of a cube is x^(3) where x is the length of one side, but the surface area is 6x^(2). This means that smaller systems will have an unfavorable ratio of surface area — through which heat is lost — to volume — through which heat is retained and transported.
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