I assume you mean a pre-dedication general public tour, and not a ward temple trip.
I don't know if typical Mormon "Sunday dress" is de rigueur for those public tours, but it certainly would not be out of place. I am sure the standard is somewhat higher than "shirt and shoes required."
If Sunday dress is required, I imagine the ticket would say that. If it doesn't say anything, you could probably get away with "business casual". They would just consider you a clueless gentile.
If you can find a set of Mormon underwear, wear them on the outside of your clothes. If anyone questions your decision, just tell them that you want to feel protected in case of an unexpected accident inside the temple.
Also a green apron and baker's hat should be worn. Tell them you're all set to bake some awesome cookies.
If it were me, I'd dress like a million bucks, so they'd know I was "successful" without them. Wear a nice suit and shoes, but to make it clear I wasn't a member of TCOJCOLDS I'd wear a bright colored shirt with no tie. Or perhaps a black shirt, w/or w/o a black tie. I'd also probably wear a few pins to subtly show support for a variety of things that I know would irritate them.
And I'd smile a lot, so they'd know I was "happy." And I'd laugh a lot, because it would probably irritate them.