The USSR built a nuclear district heating system in Gorky (now Nizhny Novgorod) but never commissioned it because of the general anti-nuclear sentiment at that time.
It's certainly possible and not even very hard (by nuclear standards) because the reactor can operate at ambient pressure.
The biggest issue is inefficiency and cost of district heating except for places like Finland. It's now cheaper to install heatpumps instead.
Bohunice Nuclear Power Plant is used for nuclear district heating.
"Upon development of a district heating supply network in the town of Trnava near Bohunice NPP, V2 switched to co-generation. Part of this system is a heat feeder line commissioned in 1987. In 1997, a heat feeder line to Leopoldov and Hlohovec was created, branching off from the Trnava line."
We don’t need any new and untested technology to solve to stop spewing out greenhouse gases. We just need to scale up current green tech. It’s not know how and technology that is lacking, it is political will.
I don't say we shouldn't do research. What I do say is that we do have all the technology we need. And more importantly, we don't have the time to wait for some future technology that potentially could solve all our problems. The climate disaster has already started (and this [0] is not "the new normal", this is just the beginning, a hint of what we should expect).
The only reason we are in this shithole is because of the lack of political will. It would have been comparable trivial to solve if we just had started 30 years ago when scientists started to yell about that it was getting urgent.
We don't need new technology, it took France only about 20 years to replace it's coal and oil based electric generation with nuclear power generation (between 1976 and 2000).
Because of lack of political will in US and many European countries we continued to burn fuels to generate electric energy.
If by "we" you mean the whole world, then we have to do a gigantic scale up of the current green tech, as current green tech produces on minuscule part of the global primary energy.
What could possibly go wrong!?!?