The only deployed thermal storage systems are in solar thermal arrays. Those have costs that aren't not competitive with nuclear, and they're still subject to seasonal output variability due to weather and Earth's inclination.
District heating systems distribute heat, usually scavenged from a power plant. They don't store heat really - they do in a pedantic sense in that heat is "stored" in the distribution pipelines, but not in the sense of a battery. And they don't transfer heat at gradients large enough to generate electricity effectively.
