Thanks for the replies! Yesterday was a crummy day in general and the heat was not helping, so I was exceptionally bitter. I don't mind sweating so much if I'm heading straight home from work... I usually ride much faster and arrive home utterly drenched. The issue is more if I have to ride into work at any time other than first thing in the morning (happens at least a few times a month), or if I am going anywhere other than straight home in the evening.

I think the rack/pannier thing is going to be my best bet other than the dodgy sauna (have been using a messenger bag). Need to figure out what options I have given I'm riding a minivelo. Yes, I believe the sauna may be dodgy in that way, given the girls I see queueing in front of the service elevators. Probably still worth investigating a shower-only option.

Shanghai's not always this hot. In winter it gets down below freezing on occasion, which is great since my apartment building isn't insulated.