Mishnah 3 in chapter 7 of Maseches Temurah. In the two previous mishnayos we dealt with the differences between kodshei mizbeach (items consecrated for the altar) and kodshei bedek habayis (items consecrated for the upkeep of the Temple), whereas here the Mishnah comes to teach us the matters in which the two are alike - items consecrated as a korban upon the altar on the one hand, and items consecrated for bedek habayis on the other.
"Ein meshanin osan mikedushah likedushah" - one may not transfer them from one sanctity to another:
The first law that applies equally to both is that one may not reassign the consecrated item to a different purpose. A person might have thought that the meaning of consecration is merely that the item is set aside for Heaven, so that people may not make use of it, but that within that framework he is free to move it from one category to another. To this the Mishnah answers no: once the animal has been consecrated for a particular korban, such as an olah, it remains an olah, and so on.
The same applies to hekdesh of bedek habayis: someone who enters the Beis HaMikdash, sees that the roof is leaking, and says, "This money of mine is given for repairing the roof" - he can no longer redirect it and say, "It would be better for me to use it to fix the faucet."
According to the Bartenura this applies in every respect, and one may not even transfer from one type of bedek habayis to another need of bedek habayis. The Rash and the Raavad disagree with him and hold that within bedek habayis there is only one general sanctity, and therefore one may transfer from something less important, such as repairing a leaking roof, to something more sacred, such as repairing the altar. In their view, what may not be done is a transfer from bedek habayis to kodshei mizbeach or the reverse.
"U'makdish nosein" - and one who consecrates gives:
The letter vav in the Mishnah here carries the sense of "however": even though one may not transfer from one sanctity to another, one may still consecrate the value of something that belongs to kodshei mizbeach. This is hekdesh erech - consecrating the assessment of its worth, and that value must be given to bedek habayis.
In other words, one who has in his possession an existing korban consecrated as kodshei mizbeach, and says, "I wish to give this too to the Beis HaMikdash" - the consecration does not take effect on the animal itself, so according to the Bartenura and most of the commentators, with the exception of the Rambam, but rather he takes on a second, additional obligation to give the value of that korban to bedek habayis.
For the sake of discussion: a person who vowed to bring an olah worth one hundred dollars, consecrated this animal to be an olah, and afterward said, "I am now giving it to the Beis HaMikdash" - he must give an additional hundred dollars to bedek habayis. The amount of the obligation depends on the manner of the original consecration:
Neder (a vow of obligation): since the person is responsible for the korban and is obligated to replace the animal, its value to him is its full worth. If the olah is worth one hundred, it is worth one hundred to him as well, and therefore he must give a full hundred.
Nedavah (a donation): here the donor takes no personal obligation upon himself; he simply says that this particular animal is a gift to Hashem. Consequently there is no responsibility here: if the animal was trampled, the one who consecrated it need not replace it, and he receives no value of a substitute. The entire economic value he has in it is tovas hana'ah - the right to choose who will merit to offer this olah, such as giving it to his grandson the kohen, who will offer it and receive the hide of the animal. Therefore, instead of a hundred the value will be, say, ten, the measure of the tovas hana'ah, and that is all he must give to bedek habayis. This is how the Bartenura learns it.
The Rambam learns it differently: one who consecrates an existing olah to bedek habayis effectively doubles the consecration resting on the animal, and both the sanctity of bedek habayis and the sanctity of kodshei mizbeach rest upon it. It does indeed go up on the altar, but he must redeem the value component - if it is worth one hundred dollars, he performs a redemption on the bedek habayis component and gives that hundred to bedek habayis. It is an unusual law, but that is what it means according to his approach.
It is worth clarifying briefly: one who consecrates something with the consecration of bedek habayis, saying, "This pen is given as a gift to the Beis HaMikdash," it is from now on sanctified to Hashem and the property of the Beis HaMikdash, and the owner has no share in it at all and no economic value in it. Therefore, if he were to consecrate it again and say, "I hereby consecrate this pen once more to the Beis HaMikdash," nothing would take effect, since he has no share in it whatsoever.
"U'macharim nosein":
Beyond the option of dedicating an object's value to the upkeep of the Temple, there is the concept of cherem, which is a gift to the kohanim. Just as a person can say, "I hereby give the value of this olah offering to the Temple," in which case his vow obligates him to pay the full value, so too if he declared it cherem - he gives that obligation of value to the kohanim, those same hundred dollars that the olah is worth.
"V'im meisu - yikaveru":
In both cases, offerings of the altar and items consecrated for Temple upkeep, an animal that died is not redeemed but is buried. We have already learned that we do not redeem a consecrated animal in order to feed it to dogs. For if someone consecrated an animal as a shelamim offering and it died before he managed to offer it - even if it had been alive and blemished and he redeemed it, his only option would be to eat it: he may not work with it and he may not feed it to his dogs. And now that it died rather than being slaughtered, it is a neveilah with no use whatsoever, and eating it is forbidden, so it is not redeemed at all but simply buried.
Tanna Kamma: The same law applies even to items consecrated for Temple upkeep, and its source is a verse. The passage in Vayikra 27, which deals with the valuation of a consecrated animal that requires redemption, establishes that the animal must be stood before the kohen. Since the requirement is that the animal stand, an animal that died and cannot stand is not subject to this valuation that determines the redemption price. In the view of the Tanna Kamma, the verse applies equally to offerings of the altar and to items consecrated for Temple upkeep: if it died, it cannot stand, and therefore it has no redemption and no valuation, but is buried as it is.
Rabbi Shimon: That verse speaks specifically about offerings of the altar, about a sacrifice, but regarding items consecrated for Temple upkeep, where the consecration goes to the Temple, there is no need for the animal to be able to stand. True, a carcass is not worth much, but it is worth something: as food for dogs, as raw material for a glue factory, and as hide from which to make a couch. Therefore Rabbi Shimon holds that items consecrated for Temple upkeep that died are redeemed. If a person consecrated a horse for Temple upkeep and the horse died, he must redeem the carcass for its full value, removing it from its sanctity and handing it over to someone who will make use of it, and the money goes to the Temple. This is because he rejects applying that verse to items consecrated for Temple upkeep.
The halachah, however, does not follow him, but rather the Tanna Kamma: even items consecrated for Temple upkeep that died are buried.
Let us clarify one point in closing: if a person had an animal that was already dead, such as a dead horse in his yard, and he says, "I hereby give it to the Temple for its upkeep" - the Temple can certainly turn it into money by selling it to the glue factory and receiving the cash, and there is no problem with that at all. The problem applies specifically to a live animal that was consecrated and afterward died.