Heat is the worst form of energy. It's super hard to extract energy at all from it. Basically, you can't extract energy from heat itself, you can only extract it through the process of heating something up. So you always need a cold component that gets heated up and a hot component that does the heating.

Without a cold component, you can't extract energy from heat.

This would work in winter and there are already heat pumps that use river water. Those are utility scale installations, though, so they don't just pop up overnight. And they'll be pretty useless in summer, when the air is hotter than the water.

Not if they don't already have the infrastructure in place. Remember that these power stations were built 30 odd years ago. No one expected climate change to get this bad this quickly even in the most pessimistic of models.

Thermoelectric is hilariously inefficient, so you can't really use it for electricity production, once it's served its purpose of turning the turbines.

What you can do with spill heat is to reuse it in district heating networks to provide hot water. And heating, of course, but there's no use for that during heat waves