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A hot interior can sometimes be caused from a faulty heater valve, it's an easy replace. So you can cool down the inside.
1963-1968 Corvette Heater Control Coolant Shut Off Valve. Found on lower RH side near firewall, be sure to check this item if you have excessive heat in passenger compartment. This valve connects in the heater hose line and has a vacuum port to heater control on dash