Check the thermostat settings on your hot water heater. If the external temperature is cold and the water heater is set to maintain a high temperature, the unit will run more than normal. Lower the thermostat and see if the unit shuts off.
Check for water leaks. Shut off the water supply at the tank and verify that no water is running in the rest of the house. Inspect your water meter after making sure no water is being used; if the meter is still registering water use, there is a leak in your water supply. This leak can cause your hot water heater to refill and heat constantly; contact a professional to repair a hot water line leak. If the meter is still, turn off the power supply to the heater to prevent a dangerous explosion and contact a professional.
Shut the water heater completely off and drain the hot water tank by opening the hot taps in your home for 10 to 15 minutes. Inspect the hot water heater for calcium or limescale buildup; this scaly buildup can cause blocked pipes and corrosion on the water heater's moving parts. Clear off corrosion and then allow the tank to refill.