Yes,You can even get really fancy pain too. I have seen some folks put a piece of diamond plate aluminum around that FB door to keep the paint in safe keeping.
Current Smokers: Backyard RF Offset and Hybrid RF Offset trailer rig with Cowboy cooker and fish fryer, always room for more........
I used regular enamel paint on mine and used high temp engine paint on ash door area and as you can see the framework on smoker side even though I used engine paint for this area it is still discolored from the heat. At one time I checked temps and at 250 f cook chamber temp my ashbox frame was 362f and charcoal chute lid was 185f.
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Grandma always said "if ya can't be handsome ya better at least be handy"