Is it still possible to plumb hot water into such dishwashers? Then the heating element have less work...
Temperature sensing is extremely simple and cheap. Bi-metal contacts have been used since the dawn of electronics, and the solid state versions are also really simple. (Making components that are temperature invariant is the hard task.)
A bi-metal contact is only good for a single temperature, I think? (can be adjustable like thermostats) (I'm sure many but not all dish-washers probably do only need a single temperature...)
My dishwasher has a scalding 75°C option.