Make sure the carburetor has the correct 3/8" thick phenolic insulator under it.
Make sure the carburetor's float hasn't become fuel-soaked. Check the float settings and make sure they're not too high. And yes, also check to make sure the choke isn't closing upon shutdown even in the hot.
Install a new inlet needle and seat in the carb.
Purchase from the dealer and install a carburetor heat shield p/n 5214 558 (it's also nice if you can get the heat shield extension 4105 070, but this is showing NLA. Perhaps your dealer is friendly enough to look and see if anyone's still got one):
Make sure your thermostatic air cleaner is working correctly so as to duct cold air to the carburetor when the engine's warm.
Install a 180° thermostat; my preference is Stant SuperStat #45358.
Make sure your ignition system is in top condition through and through.
More advanced (=more difficult and costly) heat-soak countermeasures include installing an electric radiator fan with a controller that allows several minutes' fan runtime after engine shutdown to cool down the engine bay. You can also wrap the exhaust manifold and the headpipe with Thermo-Tec wrap, which will do a lot to keep the exhaust system from heating up the engine bay.
This owner has also wrapped the intake, which is not normally done, but would add to the insulation. He has not wrapped the collector of the exhaust manifold or the headpipe, which would be a help in your situation (but probably is not needed in his big, empty '62 B-body engine bay).
