Dear Samantha Jones
I don't know of anyone who has tested this or observed it. So I'll have to think about it logically.
Sunburn is caused by UV (ultraviolet) radiation damaging the skin. If a layer of skin is destroyed then an increased flow of blood is required to renew the skin. So the damaged area becomes red.
A dead person has no blood circulating so the blood won't flow to the skin, even though it will be damaged. So no 'sunburn' I suppose.
Hmm... But I'm not sure. If you find out the right answer from someone else then please let me know.