[Piwoslaw]

Our thermostat has a dip switch to choose the tolerance: either 0.25 or 0.5*C (0.5 or 1*F). Eg if I set the temp to 19*C and tolerance to 0.5*C, then it turns on when the room temp falls to 18.5 and keeps the furnace going until the room is 19.5. As I said, this is controlled by a small switch on the back, not as a programmable function.

I don't know if this will help you, but my furnace has a maximum water temperture dial and the water temperature sensor is on the warm (output) side. I noticed last year that when this was set to minimum, then after the furnace would turn on the water that suddenly got hot would hit the temp sensor and turn the furnace off. As soon as the pump moved more water across the sensor it would cool and turn the furnace on again. This would cycle on-off about 3 times per minute. This wasted a lot of fuel. It turned out that raising the maximum temperature to just above minimum solved the problem: now the furnace turns on and keeps going until the room t-stat shuts it off.