It's so tempting, you think there has to be a way to make it work. But I haven't found one yet and I more or less gave up on it. The most practical ones that I'm aware of are in spacecraft for extreme cooling and in a commercially available generator.
If you've never seen one up close I highly recommend building a model of one and watching it run, it is complete magic compared to internal combustion engines which tend to be noisy and dirty. Stirling engines run so quiet you have to be right up close to realize it is running at all (and even then you probably will subconsciously put your hand on it to verify that it is not just your imagination).
The Philips company, when it still meant something, put together a whole slew of pilots: a boat and a bus, and an endless number of them in the lab. Fortunes have been sunk in these and with preciously little to show for it other than an extreme appreciation for how hard it is to make a really good seal.
Wurm et al's book is the standard in the field, it is very thorough and gives a very good grounding in the theory as well as some appreciation on why this is both a tempting and very hard subject at the same time. Most engines are hard to think of and relatively easy to engineer once you've thought of them. There are two exceptions, Stirling engines and Wankel engines and both have very strongly related problems. Solve the seal issue and the world will pave the way to your door with gold.
The closer a heat engine/pump gets to maximum theoretical efficiency, the lower its power density.
Odum observed[0] that (for certain linear assumptions) the maximum power density is achieved at half the theoretical Carnot efficiency. He noted that both real engines and biological systems tend to cluster around this optimum.
What's interesting, but not terribly surprising, is that this implies a fundamental and unavoidable tradeoff between machinery cost and operating efficiency.
IIRC there's a New Zealand company WhisperGen(?) that use them for power from waste heat from water heaters ...
Checking now, they seem to be used as marine power generation these days, I can't find the original site from 15+ years ago.