It's not economically effective to run a supercomputer only during peak times.
Some Nordic countries that have large district-heating systems have started experimenting with dumping the excess energy into those.
Electricity to heat is not that efficient; normally district heating systems run off of the waste heat of electricity generation. Are you talking about an example where the waste heat isn't enough to power the district heat?
Actual energy to heat is only useful in a true excess energy availability situation, but usually you'd start building up heat storage to decouple heat availability from electricity demand, which would otherwise be a problem with cogen plants. And heat storage is so much cheaper and efficient than electrical storage, so you want to run your cogen in sync with electricity demand. Once the heat storage is there, it becomes an absolute no-brainer to also use it when you have excess electricity to dump (as electric heating is 100% efficient, it's the production of electricity in thermal plants that makes electric the worst form of heating).
Desalination does seem like a good target. I think synthetic hydrocarbon production will be a good place to dump excess too. Pharmaceuticals and plastics aren't going anywhere, and I bet they'd appreciate a cleaner starting point than bitumen.
Electric cars have the obvious potential to absorb peaks. With range on recent models far exceeding typical daily use, it becomes increasingly easy to make charging dependent on supply.