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What is the make and model of your electric heater? Are you referring to a ceiling A/C heating element?
If the fan comes on, then it is most likely either the thermostat or the heating element itself. On the LP furnace, it can be due to many things. Low LP pressure at the tank regulator can make it hard to start as can a low tank volume. As it gets colder less BTUs are available from the LP in the tank if the volume is low. Keep the tank over 1/2 full to be sure. If the blower comes on when you turn up the thermostat then look for that or perhaps a bad control board. You mentioned having issues before. Sometimes when the control board begins to have a broken solder joint it can be intermittent in firing up. Please get back to me with the make and model of your furnace and I can supply more. Check all the obvious things first. Breakers and fuses. Batteries that need attention which can cause low voltage on the DC side. All these appliances take good 12 VDC power in order to operate. When it is cold out, the batteries are harder to charge and fail more often. Please get back to me with this info and I can add a manual for the furnace which can help with the diagnosis. All follow ups are included in our fee.