If the peak is predictable, there's no need for networking. The appliance equivalent of a light-timer (or a little robot that presses "start") is all that is requisite.
Certain events such a sport games or TV shows could drive the price up. That could be predicted but requires more than a timer.
For a heat pump from air the efficiency depends a lot on the outside temperature. So the best time to run it might not be when electricity is cheapest.