Hi Kepler,
Yeah, the evidence for a temple of Solomon is limited to the tradition rather than the archaeology. There have been some recent excavations at a site outside the original walls from the city which may correspond with a description of a royal palace being in a place which fits the biblical account, and that would then help further buttress the location of the temple. Mazar was the archaeologist, was billed as 'David's Palace', but it's worth reading Finkelstein's rebuttal too - he holds a very 'minimalist' position and I always find him a useful guide on how far things can be interpreted without reference to the bible. Mazar in particular has had a couple of digs where the dating seems shoehorned to fit the bible.
General point though is that even, say, Finkelstein accept that something was happening in the hills. His suggestion remains that the 40 years of David/Solomon isn't actual time so we're very much in the stuff of legends. Even if they could dig on temple mount, I suspect the remains of any pre-exilic temple would be at best some re-used masonry. If that. Don't think there's any reason to fully doubt the existence of a cult sanctuary (of some type) there though?