At Yoma 41a, there is a discussion regarding the appropriate offering for someone who causes the Temple to become Tamei? But what are we talking about becoming tamei? The utinsels the metzora touched I can understand? But can he convey tumah to the stone structure or utensils he doesn't touch? If he can, what needs to be purified, and what is the method? Also, since the Holy-of-Holies and the altar are not under cover, do we worry ever about tumas mes?
The Gemara is not referring to a person causing impurity to the Beis Hamikdash or its vessels, but rather one who defiles the Mikdash by being inside it while impure. His liability to bring a sacrifice is the same whether he actually defiles a vessel of the Beis Hamikdash or not.
He does not convey any impurity to the structure of the Beis Hamikdash, but, as you noted, he can convey impurity to certain vessels, which would mean they would have to be either immersed or sprinkled (depending on the impurity conveyed). Impurity due to contact with the dead can be transmitted in many ways, with only one of them being "under cover" otherwise known as Tumas Ohel.
All the best,