Hey there, Greengold4. I get where you're coming from. I'm very active myself - serious bodybuilder, plus I bike and hike - and I live in the California desert. Lots of heat in the summer, to say the least! Ken at Abenda offered some good suggestions. I'll offer a few more.
If you don't want to go the route Ken suggested, I suggest wearing the absolute thinnest diaper you can get away with, and then put a large pad or guard inside. That's generally a better option than going with a larger, thicker diaper (if your incontinence will allow it). Then, what I do is wear boxer briefs - I'm an UnderArmour guy - over my diaper, both to support the weight of the diaper when I wet, as well as to muffle any sound the diaper might make. In addition, the UnderArmour also can soak up a little bit of pee if my diaper leaks, which isn't common but does happen occasionally.
Finally, I strongly suggest staying hydrated at all times. I know it's kind of counter-intuitive for those of us who are incontinent, but it's hugely important nonetheless.
Good luck, and PM me if you have any questions or just want to vent.