Shekalim, Chapter Eight, Mishnah Six
This mishnah discusses most holy sacrifices such as burnt-offerings, guilt offerings or sin offerings which were defiled either within the Temple or outside of it. That these sacrifices must be burnt is clear and agreed to by all. However, Bet Shammai and Bet Hillel disagree whether the sacrifice is burned inside or outside of the Temple.
Meat of most holy things which was defiled, whether by a principal uncleanness or by a derived uncleanness, whether inside or outside [the precincts of the temple]:
1) Bet Shammai say: it must all be burnt within, except when defiled outside by a principal uncleanness.
2) But Bet Hillel say: it must all be burnt outside, except that which was defiled by a derived uncleanness within.
Section one: According to Bet Shammai all of these unclean sacrifices must be burned within the Temple precincts, in the place within the courtyard where the ashes were placed (called the Place of the Ashes). The only exception is a sacrifice which was defiled by a principal uncleanness while it was outside of the Temple. Since this sacrifice acquired a more serious form of uncleanness it is not brought into the Temple. However, if it had only become unclean through contact with a derived uncleanness, it is brought in and burned in the Temple.
Section two: Bet Hillel hold that all of these sacrifices are burned outside of the Temple. Anything that was made unclean outside the Temple is not brought inside. Furthermore, they hold that if it came into contact with a serious form of uncleanness within the Temple, it must be brought out and burned outside of the Temple. The only exception to their rule is that if one of the most holy sacrifices became impure with a light form of purity within the Temple, it need not be removed and may be burned within the Temple.