Two things I've found that really help with this are:
Play with the sax upright. I don't know about anyone else but I have a habit of leaning forward while playing.
Assuming you're not playing an open air gig, allow the sax to get up to room temperature before you start playing. As it's mostly condensation, a warmer instrument creates less moisture. I've just reread your post - do not stick it on the radiator to warm up! Let it acclimatise naturally rather than using a heat source.
Of the two, not leaning forward is probably the one thing that will make the biggest difference, It doesn't mean you should never lean forward, but rather for it to not be your default playing position. It has the added benefit of giving the audience better eye contact at shows., too. After all, there's nothing worse than watching a band where they're all staring at the floor and all you can see are the tops of their heads.
The other thing I've noticed; if I'm playing really quietly, the lack of air flow seems to make moisture noticeably worse. Ironically, playing stupidly hard (when you get carried away
or you're battling a deafeningly bad sound mix on stage) seems to create the same problem.
