They typically have a very powerful 2.5 kilowatt heater they run in bursts - for like 5 mins when prewashing, for like 10 mins when starting the main wash, and like 10 mins again when drying.
In between those times, the machine uses only ~60 watts for pumps.
I have often pondered what a world of machines designed to meet solar output looked like - and for a dishwasher it would involve the heater being modulated to match the solar output (and knowing that sometimes the wash cycle would take longer if a cloud was overhead so heating was delayed by a half hour).
Concrete costs far fewer $$$'s than batteries do, per kwh of heat stored, it also doesn't require inverters, balancing or safety systems, ad lasts millions of cycles rather than thousands.
You can still slowly heat it up to 70 or 80°C and just add some extra heat on use, but that will still leave a lot of immediate power to deal with.
However, since my array is currently 4.4kw at 3 in the afternoon, a 2.5kw burst isn't a problem.