Why? Just overheat the water circulating through the district water system when you can. People's thermostats will simply turn off sooner, leaving more heat in the water.
Then later, you underheat the water, and the city's various thermostats turn on a bit longer.
The risk is that you underheat too much, and people compensate by plugging in their own heaters during underheating. And underheating will occur during expensive energy periods, so this will exacerbate periodic energy shortages. But overall this could work to store a ton of energy - there's a huge volume of water in a district heating system's pipes.
Then later, you underheat the water, and the city's various thermostats turn on a bit longer.
The risk is that you underheat too much, and people compensate by plugging in their own heaters during underheating. And underheating will occur during expensive energy periods, so this will exacerbate periodic energy shortages. But overall this could work to store a ton of energy - there's a huge volume of water in a district heating system's pipes.