At the powers involved you might melt quite a bit of the ground :). But some heating plants for centralized house heating do have electric water heaters, which are used, as soon as the electricity spot price goes below a certain number - the rest of the time they heat with gas.

These spikes would go mostly away, if more coal plants get replaced by gas plants which can be switched off very quickly. I guess, as soon as there are more of those days, this shift is getting financially attractive.