Our electricity stopped because we fell three months behind on our utility bill, so we had to spend the hot day without an air‐conditioner.
過ぎる is to surpass... 過ごす is to spend time on... for some reason. I suppose if you surpass something or someone, you must spend time to do it.
The reading is the same as 過ぎる. Time to surpass this kanji? Or, maybe it's time to spend time on it instead.