You are not allowed into a Mormon temple if you are not Mormon.
My teenage daughter has friend who is Mormon. My daughter used to play on their girl’s basketball team, even went to their so called basketball camp for several weeks during a few summers. She was invited and attended their services multiple times on Sundays. I don't know if Sunday services are held in "a Temple" or some other structure, but my daughter did go into the worship building. I do not know enough about Mormons and their rituals so I wonder exactly what type of building they took my daughter to if she would not be allowed into their temple.
Several other comments; it was okay for my daughter to attend their services but their daughter was forbidden to go into my daughter's Catholic Church. Also their services lasted for like 3 hours and my daughter described it more like a social than a service.
PS, my daughter is very doubtful of a Supreme Being and says only goes to church with my wife to keep her company. My wife on the other hand likes church and it would be detrimental and hopeless for me to try sand convince her otherwise. Although; I keep planting seeds.