Beitzah, Chapter Two, Mishnah 5. This mishnah presents a dispute between Beis Shammai and Beis Hillel that revolves around a single question: once kindling a fire has been permitted for the sake of cooking food, is it permitted for other forms of benefit as well?
The view of Beis Shammai:
"Lo yacheim adam chamin l'raglav, ela im kein re'uyin lishtiyah" - a person may not heat water in order to wash his feet in it unless that water is fit for drinking. In other words, the heating must be done for the sake of drinking, and once the water is before him for that purpose, he may also use it to wash his feet, and certainly to wash his face and hands. Some hold that he must actually drink a little of it.
The view of Beis Hillel:
"U'Beis Hillel matirin" - it is permitted to heat water even for the sole purpose of washing one's feet, and certainly for the face and hands. The basis of this leniency is the principle "since kindling was permitted for a purpose, it was permitted even not for a purpose": since kindling a fire was permitted on Yom Tov for the needs of eating, it was permitted even when not for the sake of eating, but for some other benefit to a person.
Some understand that Beis Hillel permitted specifically washing the hands and feet, because this is a need common to everyone; but washing the entire body, which is not considered a universal need, was not permitted. And if the water was heated the day before, the halachic authorities disagree: whether one may wash the entire body on Yom Tov, or only the face, hands and feet.
Kindling a bonfire:
The mishnah concludes with a ruling attributed to the view of Beis Hillel: "Oseh adam medurah u'mitchamem k'negdah" - a person may light a bonfire and warm himself beside it on Yom Tov. Even though this is not a need of eating but a different form of benefit, Beis Hillel hold that with regard to the labor of kindling on Yom Tov, other forms of benefit were permitted as well.
In summary: in this mishnah Beis Shammai and Beis Hillel disagree about the scope of the permission to kindle on Yom Tov: according to Beis Shammai one may not heat water unless it is fit for drinking, while according to Beis Hillel, since kindling was permitted for the needs of eating it was permitted even not for that purpose - and from here comes the permission to heat water for washing and the permission to make a bonfire in order to warm oneself beside it.