In the midst of a prolonged arctic blast, the problem of a furnace that will not turn off is certainly preferable to the specter of a furnace that will not turn on. However, a furnace that doesn’t stop-and-start, or cycle, is problematic. While it’s certainly plausible that your furnace is perpetually running because it’s simply not able to supply the heat demanded by the thermostat, continuous operation of a furnace over a protracted period causes undue strain on the machine