Incorrect Timing Adjustment causing heat issues?

Three things need addressed here:

1. Why are you setting your base ignition timing to anything ATDC? Spec timing for a '65 273-2bbl is 5° Before TDC (manual transmission), 10° Before TDC (automatic transmission), without the vacuum advance hooked up. Retarded timing (after TDC) causes hot running by a very simple chain of events: spark occurs late, so fuel/air mix still burning when exhaust valve opens, so cylinder head heats up extra-hot, which heats up the coolant…and exhaust manifolds and headpipes heat up extra-hot, too, which heats up the underhood air.

2. It sounds like you have significant vacuum going to the vacuum advance at idle. You shouldn't. Make sure the vacuum advance is hooked to the correct port on the carburetor, and if it is supplying significant vacuum at idle, either that's another problem being caused by the incorrect base ignition timing (retarded timing causes slow idle, so you crank the throttle plates open with the idle speed screw, which uncovers the spark advance port, sending vacuum to the distributor) or there's a problem with the carb (throttle plates not closing correctly). Find and fix this problem.

3. Why are you so fixated on a Clean Air Package your car does not have?
I am not fixated on it. All I am saying is that the car when I purchased it, was firing after TDC at idle. At that point in time I believed it needed to be there and was correct. I know that it is not and I moved it 10 degrees BTDC.
Vacuum canister is hooked up to ported not manifold and when I set it before taking it to the shop that did the work it seemed fine. (I could remove and plug the port and not notice any difference in timing at idle.)