That's too large of a temperature fluctuation. Is there no way to keep the temperature constant?
If you kept your hedgie in there, and they're used to say... 78F and it randomly dropped down to 72-73, you may get a hibernation attempt. Do you have the cage already? Perhaps stick a thermometer in there, and test out different ways to insulate the cage (like covering up some of the walls, perhaps a blanket over the cage at night, etc etc)
So unless you can find a way to keep the temperature constant, I would have to say "Yes", get a CHE to keep the temperature from dropping too low.