Single-home scales are an unsuitable scale for the generation of thermal power. It’s too powerful to be practical for small Thermoelectric or Thermionic generators, yet too small for steam turbines.
There are solid-state heat-to power systems however, their effectiveness is quite low except for a high temperature source of heat. Moving heat through what’s basically an insulator is extremely difficult for creating large quantities of power. Charge a phone? Easy! However, running a microwave and vacuum is extravagant and expensive.
Steam turbines are simply too complicated for non-industrial use and aren’t scalable down.
The one thing that springs to the mind is the idea of a stirling engine They’re quite flexible in terms of not having a particular heat source, and also have only a few moving parts, which means they can take advantage of some advantages of solid-state systems.
In terms of micro-combined power and heat is concerned, I believe it is generally more sensible to utilize a conventional electrical supply (eg natural gas generator) to generate heat rather than trying to affix the thermal generator to an existing source of heat. It is easier to heat your home with engines radiators than to power an engine from your central heat source in your home.