Alleyways To Torah

Maybe its' talking about prior to bringing it as a korban in Yerushalayim.

Such as cook it first and then bring it to Yerushalayim

Perhaps "chamei Teveriah" is just a general term for boiling water that comes from the ground, anywhere.

Or maybe, there is the midrash that when the mashiach comes, the borders of Jerusalem will expand to include all of Eretz Yisrael...

yeah, the fact that the actual cooking is done in teveria seems lav davka....

It is always possible to suggest that perhaps the חמי טבריה were brought to Jerusalem, but the likelihood of them staying hot enough to cook the קרבן פסח is remote. As such, if the גמרא is to be taken literally, we must assume that רב חיסדא is in fact considering a case where it is מותר to bring the קרבן outside ירושלים. Such an instance can only be possible during the time of היתר במות, when קדשים קלים could be eaten in any city within Israel (see זבחים קיד:, for instance). So, a person could have done the הקרבה in say גבעון (where there was a במה) and then brought the קרבן (which is קדשים קלים) home to טבריה to cook in the חמי טבריה. Of course, this still is a little דוחק, as why would רב חיסדא suggest a case that not only wasn't something that could have happened within the last 1500 years of רב חיסדא generation, let alone any time in the future. But alas, the גמרא tends to be analytically exuberant at times.

Reviewing the sugya, I retract my answer. If one cooks on shabbat in chamei teveriah, it is not considered bishul, because bishul refers to fire and other sources of heat besides chemical fire are not considered to be a mode of bishul on shabbos. Which is why one can use a solar oven or a nuclear oven or a microwave oven on shabbos. It is only because of a gezeirah that one cannot use such modes as they are similar to water cooked with fire. But mikar hadin, as long as one is using a microwave or the sun, which is what chamei teveriah are, one is perfectly fine cooking on shabbat with this. Therefore, when it comes to korban pesach, the din should be the same, suggests the gemara. So if one cooks a korban pesach in chamei teveriah, that is a solar heater, it ought to be that it is not called bashel mevashel bamayim, because there is no heat the way one normally cooks with water, namely from a fire. Looking at things this way, the gemara's question is as follows: why is it that on shabbos one is patur if he cooked using chamei teveriah? Answers the gemara, because one needs toldat eish, and since chamei teveriah is not toldat eish, one is not chayav for cooking with chamei teveriah on shabbos. But, when it comes to korban pesach, even though it is not toldat eish, one is chayav not because of mevushal but because of ki im tzli eish. That is to say, indeed it is not mevushal, but it is not tzli eish either, and that is the chidush of Rav Chisda.