> Lots of home appliances generate lots of heat (clothes driers, ovens, refrigerators, ...) that is currently vented to the atmosphere. it'd love to capture that and use it to "charge" the hot battery.

I've seen systems that use waste heat from central A/C to heat a swimming pool. In addition to the condenser they have a heat exchanger connected to the coolant line. Pool water is pumped through the heat exchanger and back out to the pool.