I bike half an hour in the summer in this hot and muggy area and as long as you remember to rinse your pits and change out of your sweaty clothes when you arrive you won't be stinky. It's something I worried about when I started biking, but it really hasn't been an issue at all.

The stinky part comes from those sopping wet clothes you changed out of and had to hang up somewhere. Hopefully not in your office.