Dear Father Deacon John,
The underclothes were indeed made of fine twined linen, but there's more to it than that. Unlike the vestments, the linen underclothes could only be worn once. Here's how it worked:
A fresh set of underclothes for the High Priest was made each year. Upon arrival at the Temple, the High Priest would lay aside all his own garments, take a complete bath, and then put on the new linen underclothes and the vestments. He would then, with the appropriate sacrifices and prayers, enter the Holy of Holies.
Upon emerging from the Holy of Holies, he would lay aside the vestments and the underclothes, take another complete bath, and don his own garments again. The vestments were carefully put away, and later gone over in case any tiny rent or other damage had occurred.
The underclothes, however, were carefully washed, and the water from this washing (as well as the water from the High Priest's second bath) was poured on to the Temple gardens. The washed and dried underclothes where then unravelled and the fine twined linen was carefully dried, cut to the appropriate lengths, and used as wicks for the Temple oil lamps in the Holy Place.
The point of all this was that nothing which had been inside the Holy of Holies could be returned to any less sacred use.
Incognitus