Honeywell’s Winter Watchman provides an easy way to monitor faulty heating equipment. Perfect for when you're away from home or even for a vacation house, the watchman plugs right into a standard wall outlet. You set the unit between 30°F and 60°F (ideally about 10°F less than the thermostat’s setting). Then plug a light into the outlet on the watchman.
If something goes wrong with the heating system, and room temperatures reach the setting on the watchman, the light (which must be left in the ‘on’ position) will turn on. Place the light near a window and find a friendly neighbor who’s willing to glance at the window/light from time to time. Should the light ever go on, there would likely be an issue with the heating system that requires attention to avoid any freeze-ups in the house.