Per this answer Moshe and the Red-Hot Coals Moshe Rabainu took the coals and placed it in his mouth and his mouth got burned. It does not mention that his hand got burned. Did his hand get burned or not? If it did, why is it not mentioned, if it did not, why did only his mouth get burned?
The reason why Moses mouth got burned was to atone for the milk of the non jewish women that touched his tongue. His hand did not get burned because it did not require atonement.
I saw this in some book, i think Vedibarta Bam.