I think the heat that a thin coat of paint will retain would be negligible. The benefit of protection from the elements outweighs the down side...plus it looks good! What are you thinking: black? Body color? "Cast iron" color?
Make sure the drums are CLEAN...sand blasting is good. There are some really good coatings available nowadays...I like VHT products.

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If you can't fix it with a hammer and screwdriver, you need a bigger hammer.
1965 Chevy C10