Potential mining efficiency?

So I know that Bitcoin mining rigs generate a lot of heat. So they came out with a Sterling engine. Apparently it is capable of turning heat into electricity. Now I am not a miner or anything I'm just a thinker. My line of thinking was using the Bitcoin mining rigs to generate heat and using the Sterling engine to absorb that heat and turn it into electricity to feed the Bitcoin mining machine. Now there might not be a whole lot of electricity given back to the system but if it gives back 20% would that be a 20% reduction in how much energy you're using to mine? The item is called a thermo acoustic Sterling generator. It's kind of expensive so there's roi to think about but who knows maybe someone out there can use this to make their systems better. And if it does end up working maybe it might help with people's views on bitcoins energy intensive use.