If we assume the numbers for a sort of medium-size nuclear plant, we've got a total power generation of 500MW.

Dumping that kind of power is... hard.

If I haven't missed an order of magnitude, that's enough to boil an Olympic-sized swimming pool in about 25 minutes (500MW to boil 2.5ML of water, assuming STP).

So you'd either need to build and maintain the infrastructure to burn that kind of energy when it isn't needed (not cheap) or just sell the power at a loss (likely cheaper).