No, your scalp can get sunburned and, if the heat is great enough, your brain can “cook” from the heat and actually suffer from blistering, edema and fever. However, it is the ultraviolet light from the sun that causes sunburn, and the pain from that burning your scalp would cause you to react before your brain would suffer any real damage.
I suppose we could tie you down with your scalp facing the sun, ignore your screams, and slowly adjust your position throughout the day in order to obtain the maximum exposure. However, as Outlierrn pointed out, “it’s not likely to be studied”. LOL
FWIW brain and skin come from the same tissue embryologically: the ectoderm. Early on some folds in to be become the tube that gives rise to brain spinal cord and nerves.
There are cases of melanoma originating in the brain, mostly from the meninges (the covering) but also from pigmented cells in the meat of the brain. Rare but occur.
And. Not sure about “sunburn” per se, but the mechanism by which UV radiation damages DNA, which then results in cancer, would be the same for all DNA exposed to it.