A few years back, some professors from Hebrew University made an unauthorized tour of the tunnels beneath the dome, believing they'de been made by the Israelis while the old temple stood. Turns out they were right. They also found that the temple had stood beside where the dome now sits, so the destruction of the dome is not a prerequisite for building the new temple.
When the Israeli security forces that patrol the area in agreement with several Moslem entities found the professors, they politely ordered them out lest their presence start a war, but of course the security, being Jewish, wasn't harsh with them.
Right now, no Moslem would be happy with having a Jewish temple beside their second-holiest site, so I'm thinking there'll be some kinda treaty brokered to allow it. Perhaps even the antichrist will swing it, as nothing in Scripture says that temple must be built before he comes.
So, I believe the next significant prophetic event will be either the building of that temple or the coming of the beast/antichrist to power.