The radiative heat loss from the 500-meter diameter spherical habitat would be at least 3.282 million watts. If each human radiates 100 watts on average then the ship would absolutely require 32,820 people on board generating body heat to keep the ship warm.

On the other hand the heat that those people generate comes from the food they eat, which comes from plants, which grow under lights, which are electrical. The electricity is generated by steam turbines run from the heat of the nuclear core.

This is a closed habitat. The ultimate source of *any* heat, whether from human activities, or from electrical appliances, is the nuclear core. Energy is conserved. Whatever heat escapes is immediately replaced.