I recall paying ~$22 for a new heater core for my 1965 Dart maybe 6 years ago. I got it before I needed it, probably an ebay deal. Re refreshing the heater box innards, search for my post repairing two 1964 and one 1965 boxes. The vary inside. I suspect the 1963 box is much different since there is a firewall bump which interferes with some engine swaps.
