Why did Yehuda want Tamar to get burned on fire?

Some opine that Tamar wasn't meant to be burned to death but rather the punishment for those thought to be prostitutes, was to brand them with a specific sign for embarrassment (Ba'al HaTurim and R. Yehuda HaChasid). The midrash explains alternatively, that Tamar was from the family of Shem and Malchitzedek who were the kohanim of the time, and there is a death punishment for the daughter of a kohen who does prostitution (which Yehuda thought that she did, see Yayikra 21, 9).