The present invention relates to a method of managing a supply of electrical power to an appliance that is delivered by means of at least a first battery and a second battery, said method comprising the following steps: powering the appliance by means of the first battery so long as said first battery has a level of charge sufficient for powering the appliance; when the battery has a level of charge that is insufficient, powering the appliance by means of the second battery; and powering the appliance with both of the batteries in parallel when the levels of charge of both batteries are substantially equal and insufficient for it to be possible to power the appliance using a single one of the batteries. The invention also relates to an electrical power supply circuit for implementing said method, and to a method of powering an appliance when cold.