It seems that the clones and other officers did have limited access to the Temple during the war. They did hold meetings in the Temple, in various briefing rooms, and we do see clones walking through the halls, usually in the company of a Jedi. Since security was so tight during the Clone Wars, and since typically only Jedi and authorized visitors were allowed in the Temple, it is probable that they didn’t have access to the whole place, certainly not without an escort. (Of course, there are some areas of the Temple that are strictly off-limits to outsiders, even some that not all Jedi were supposed to be in, so the clones would not be allowed there.) Visits were not strictly limited to necessity, either. A number of clones and officers, including Tarkin and Yularen, attended the funeral of the Jedi who died in the bombing of the Jedi Temple Hangar.
Hope that helps!
~ Jacen