I took a dump (my first ever unplanned) in Alpine a few weeks ago while agressively pushing off in my empty solo canoe, shaking one foot (to get some of that wetfoot water off). I just gathered the floating debris, emptied the canoe, got in and paddled away. The water was a bit cool, but I was in it only about a minute, and the air was warm. I wouldn't worry too much about the water temperature for a while...

I was dressed entirely in synthetics, mostly nylon and acrylic, and was mostly dry after about 15 minutes of paddling. I dress appropriately  ;).

I am usually okay in conditions that have other's teeth chattering - your mileage may vary...

-pat