And I guess you can just shut it off in summer? Nuclear normally sucks for fluctuating demand, but presumably a 6 month on/off cycle is slow enough to work.
I assume the design is something to the tune of "put a reactor at the bottom of a water filled pit, put a big heat exchanger at the top, pump fluid through the heat exchanger and into the city's heating system and let convection do the rest"
I'm sure with some creative engineering you could do some tricks with attaching something of a specific density that changes with temperature at a rate different than the cooling medium to your control rods you could have a system that self regulates based on the temperature of the water being input (control rods sink when temperature increases) so the system self regulates output.