A vehicle includes a heating system to selectively heat a vehicle device structured for contact by a vehicle occupant or for the occupant to view surroundings outside the vehicle from inside it. In one form, the vehicle device is a steering wheel, and the heating system encompasses a vehicle power supply electrically coupled to a rechargeable energy source to energize a heating element that together increase device temperature more rapidly than with just one of them alone. The heating system detects depletion of the rechargeable energy source and recharges it with the vehicle power supply, while increasing the temperature more slowly because the heating element is only being energized by the vehicle power supply. If the temperature is greater than or equal to a target level, energization of the heating element includes some form of time-varying modulation to approximately maintain the temperature target level.