What is appropriate clothing for my example? I'd guess most appropriate would be naked, though I'd still be drenched. There is no clothing that can fix this.
I love riding bikes, but it has never been a feasible solution for my transportation to work, given that I don't want to arrive looking and feeling disgusting, drenched in sweat. I could handle your cold, though. Perhaps you've never experienced extreme humidity coupled with high-90s.
You could still find a place close by where you could rinse off and clean up quick before heading into the office.
There are an innumerable number of ways you could make it work if you actually wanted to.
I can respect that it's far more inconvenient for you than it is others, and that may be enough of a hurdle to just never make it worthwhile.
As far as the humidity and high 90s, the Land of 10,000 Lakes gets our share of shitty weather. It takes a real commitment to continue through it.