Going 'full nuclear' without capping the per-capita energy budget is still going to release a very large amount of energy. Besides that heating in many places is based on natural gas. Then there is the per kilo-watt hour cost of nuclear energy which is way higher than solar or wind when taken over the full lifetime of the installation including the eventual cleanup / disposal.
Nuclear energy is an option but it isn't the only option and it has serious drawbacks, just like every other option on the table today.
The best thing we can do is to limit our consumption. But that's easy to say from the point of view of the developed world, where consumption is excessive. It will be more than offset by the developing countries gains leaving us with a situation that is net worse than things are today even if we do our best. This is not a simple problem and naive one sentence solutions are not going to get us to a sustainable situation.