Bais Shammai says you can bring a karban Shelamim without doing Semicha [the mitzvah to lean on the korban] but a karban Olah cannot be brought. Bais Hillel says you can bring both Shelamim and Olos, and that you can do Semicha.

Beitzah 2:5

Bais Shammai says you cannot heat up water just to wash your feet unless the water is drinkable. Bais Hillel says it is always permitted. Also, it is permitted to make a big fire by which to keep warm.