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Sorry about the second post.

First, I'm curious what happens to the heat generated at the hot end
of a Stirling refrigerator? Is it just lost to the environment? If
so, wouldn't it be more efficient to use it to run a second engine?
(It obviously wouldn't recover that much power, but it should
recover some... right?)

Second, I can't find much good information on the current state of
rotary Stirling engines. I want to know if there have been any
built that are purely rotary (no pistons)? I know there are some
that use a rotary displacer, but they still use a linear power
piston.

Thanks again.

Stirling refrigerators ultimately dump the heat to the enviornment. In cryogenic systems the Stirlings are cascaded but the heat is ultimately dumped to the heat sink of the enviornment.

There are a few demonstration models with rotary displacers which use a lineat power piston. There is one with two displacers and one double actiong power piston. There was one completely rotary engine project but to the best of my knowledge it is currently on hold.

There are a lot of industrial processes which generate waste heat. The fact that Stirling engines can be made to run on low temperature differentials has attracted interest in various circles for reclaiming some of that waste heat, however I think the economy of scale tends to make reclamation of waste heat prohibitively expensive in many situations. In large industrial processes, such as smelting and glass blowing and other high-temperature work, I believe there are companies which have found cost-effective ways to reclaim some such waste heat.

I seriously doubt a home refrigerator, Stirling-based or not, generates enough heat to be worth the cost of reclaiming. A hobbyist might try it, but it won't turn into a widespread phenomenon unless it is economically viable.