Nuclear energy does not solve the heating part only because most of the existing nuclear plants have not been designed to provide heating, where gas heating was already in use.
There are many parts in Europe where the homes are not heated by gas, but by the waste heat from the local power plants, regardless whether they are gas-based, coal-based or nuclear.
Any existing nuclear plant could be converted to also provide heating for the nearby houses, if the infrastructure of plumbing for the transport of hot water would be built.
However, the last part of the heating infrastructure, where the hot water pipes would have to be passed through the house walls and through the walls of all rooms, would be extremely costly in comparison with an electric heater, even if the operating cost would be lower.
So it is very unlikely that such a conversion would ever be done to already existing houses, even if it is possible.
Heat pumps would have much lower installation costs, while still being more efficient than resistive heaters.
There are many parts in Europe where the homes are not heated by gas, but by the waste heat from the local power plants, regardless whether they are gas-based, coal-based or nuclear.
Any existing nuclear plant could be converted to also provide heating for the nearby houses, if the infrastructure of plumbing for the transport of hot water would be built.
However, the last part of the heating infrastructure, where the hot water pipes would have to be passed through the house walls and through the walls of all rooms, would be extremely costly in comparison with an electric heater, even if the operating cost would be lower.
So it is very unlikely that such a conversion would ever be done to already existing houses, even if it is possible.
Heat pumps would have much lower installation costs, while still being more efficient than resistive heaters.