Modern heat pump dishwashers will heat water on 110V just fine, but you are looking at 3 hour wash/dry times anyways. My Bosch isn’t connected to hot water and even has a sanitize mode.
Bosch dishwashers have something they call a “heat pump” that is a water pump that also heats the water with resistance heat. It’s not any more efficient than the normal heating coils in every other dishwasher, and it isn’t a “heat pump” that uses a refrigeration cycle (as one would use to e.g. heat their house).
We’re talking about heating the water, not drying. The discussion started with regards to energy used to heat water vs. using water from the hot water tap.