Why does my furnace run periodically when the thermostat is off?
This is one possibility, from my distant past...  In a house with hot-water heating that I lived in as a teen, the boiler and hot-water heating were controlled in a different way:

Whenever the water in the boiler dropped below a certain temperature, the burner came on and heated the water in the boiler jacket.  This would go on as long as the system was turned on, winter, summer, whatever.  None of this water circulated to the radiators, until...

When the house thermostat called for heat, the circulating pump came on and pumped the hot water from the boiler around to the radiators.  Of course, if the pump returned cold water from the radiators to the boiler jacket, the burner would eventually sense this and come on to warm the circulating water.