Despite the name, cold fusion is not cold, as it is described repeatedly here.
When Killer Frost is attacked by cold fire and she comes to S.T.A.R Labs to treat herself, Barry just wraps a dry bandage around her arm on the area that was burnt. He should have put a burn ointment on it to lessen the burn. Usually, such upper skin fire are kept open and only some ointment is applied; flow of air is can the soothe the pain of a burn.