A good suspect in that year is the pick up coil in the distributor. They have a tendency and reputation for going bad. Where are you getting power for the choke coil. If it is an original Ford type carb, the voltage should be comming from the field connection of the alternator which is about 7V. IF someone has moved it to a 12V connection, it will overheat. Also, on a Holley carb and some others, there is a path for drawing air thru the choke from the inside of the carb to help cool it off. If the path is clogged or on carbs that use a small vacuum hose connection and the hose is disconnected that will also cause the choke coil to overheat. The choke coil normally gets hot, but should not get so hot that it causes a discoloration of the cover where the voltage line is connected.
Good luck,

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