Het is a shortened form of heated and has been used that way since the 14th century. That simple sense of het up as heated up is first recorded in the US newspaper The Freeborn County Standard, July 1884:
"Set it right down here by the fire Susan, so 't'll get het up before you knead it into loaves."
The first record I can find of someone using het up to mean agitated is in a work by the American physician S. W. Mitchell in 1886:
"I don't het up easy."