[lambdatronics]

No-moving-parts is probably not realistic - the core would be much hotter than the radiating surface due to the thermal resistance of the shielding. More likely, you would have a working fluid to transfer the heat. Most nuclear reactors operate at much lower temperatures where TPV wouldn't be efficient or cost-effective. It's certainly possible to go much higher. Nuclear-thermal rocket propulsion tests ran with exhaust temperatures up to ~2200 C [0]. Whatever fluid is used, you would need to avoid radioactivity in it, b/c that would probably degrade the TPV. Also you would probably want to avoid having heat exchangers because each one incurs a temperature drop. So helium would fit that bill. That's what the "high temperature gas reactors" use [1]. IDK if helium-compatible plumbing/pumping could be made to work at >2000 C though.

Edit: BTW, there are radioisotope thermoelectric generators used for space applications primarily, but they are not true nuclear reactors - they produce short-range radiation that doesn't require much shielding. Nuclear reactors produce neutrons and gammas that require thick shielding.

[0] https://en.wikipedia.org/wiki/Project_Rover#Kiwi_A

[1] https://en.wikipedia.org/wiki/High-temperature_gas_reactor