You need exactly the same energy to warm your house whether it is insulated or not. You just need more total energy to get it up to the temperature you want if it isn't insulated because while you are heating your house you're also heating up the outside. The squirrels will appreciate that.
So we're just ignoring that heat flow is time dependent? Cool....I'll let my electric company know that I'm pulling insulation from the walls and to keep my billing the same.