All modern dishwashers do indeed have some type of water heater.

Additionally, your Euro is showing. American dishwashers are almost without exception designed to be connected to a hot water line rather than cold; Typically your home’s water heater is more efficient (or at least cheaper) at heating water than the dishwasher itself is, and certainly faster since the majority of homes have a storage tank heater that can be expected to already be full of hot water. The less heating the dishwasher has to do to the water the better it’s energy consumption rating will appear, which the manufacturers love. (Offloading the energy requirement for heating the water to your central water heater also shifts the cost/blame to the water heater and away from the dishwasher, allowing them to put a smaller number on that yellow Energy Guide label, even if taken from the big picture view this is prima facie bogus.)