A rechargeable backup electric heating system includes a rechargeable portable electric heater, multiple rechargeable battery packs, a rapid recharging circuit, and one or more high capacity storage batteries, from which the battery packs are recharged. The rechargeable portable electric heater has a design power output of P watts, which is determined by the BTU/hr of heat output required to maintain a target temperature in living space under prevailing outdoor temperature conditions. There are n sets of rechargeable battery packs, each having a weight of B kg. At any given time, one of the battery packs is within or attached to the heater and serving as its source of electric power, and (n−1) battery packs are being recharged by the storage battery through the recharging circuit.