What potential Halachic issues might there be (if any) with heating a knife on Shabbos or Yom Tov to help it cut through a frozen cake? The heating could be accomplished in a number of ways, including but not limited to:
- heating over a burner
- putting it in the oven for a short while
- running it under hot water
(Another equivalent case might be heating a spoon to help scoop ice cream.)
A good answer should provide sources that discuss the background of the Halachic problem that you think might apply to this case, and explains why you think it applies here.