220° is NOT overheating. I wouldn't worry about it. Just for comparison, the stock fan switch, from the factory, in one of my other cars (83 Z28) is set to 235°. In other words, in the factory's opinion, the engine does not even begin to need cooling until it reaches that temp. And furthermore, the fan shuts off at about 210°; which means that that's all the cooling it needs.
And it doesn't matter that it's a later model car, or an electric fan, or any of that; temp is temp, water is water, castings are castings, no matter the age or shape of the sheet metal surrounding them.
The boiling point of water is 212° at 1 atmosphere. At 1 atm, the boiling point of water/antifreeze mixture is around 235°. At 17 psi, typical radiator cap pressure, the boiling point of water/AF mixture is at least 20° higher than that. So, if your cooling system is properly maintained, "overheating" doesn't occur until somewhere well in excess of 250°.
So don't worry about it, do what you need to do; just make sure you have a good radiator cap installed and a suitable coolant mixture in it, like 60/40 or 70/40 water to AF.