I happened to be down in the basement a short while ago and heard the furnace turn on and off after just a few seconds. About a minute later it came on and this time it stayed on for about 15 seconds and then it shut off. This has happened before due to a dirty flame sensor, so I assumed it is probably due for a cleaning again. But, I went upstairs and checked the thermostat and it's set to heat at 73 degrees, and it's showing the air temp is 74 degrees! I'm pretty sure it normally has to drop down to 71 before the heat comes on, yet something triggered it somehow. Could this be a faulty thermostat, and if so could this explain the start and quick stop too?
You probably have a boiler that heats water (or steam) and then pumps it through the house to radiators or baseboards. The boiler needs to keep the water heated to a certain temperature so that when the thermostat calls for heat, the boiler can pump the water (at the design temperature) through the house.
So, the boiler will "kick on" from time to time to heat the water.
Also, some boilers can heat your potable hot water too (through a heat exchanger). It could be "kicking on" to heat your hot water.