And do what with it? You can't use heat to do work without there being temperature differential in the system. Maintaining that differential requires keeping your cold side cold, which means it still must dissipate its heat. In space you would have exactly the same problem doing that as just radiating that heat in the first place. Once your system reaches equilibrium between its hot and cold sides, no work could be done with that heat energy. It's just a radiator with extra steps.

If capturing heat energy to do something with it did not require sinking the waste heat from that selfsame process someplace, every satellite in orbit would already be covered in Peltiers or similar.