This is a fun subject... a year or two ago I was riding my racing bike when it started raining. After a short while I decided to seek shelter under some trees that were along the road near a bus stop. I think there were about six or seven people standing there, either waiting for the bus or taking shelter there. At that point, my shirt and legs were already pretty wet, but the upper part of my shorts were still dry.
At that point I really had to pee, but did not dare to let it go at that point. After about five minutes the rain really started to pour down, and big drops were falling on me from the leafs, that were by then saturated with water. Because of the rain, visibility was also less and there were no other people anymore on the street, I decided to let it go and let the pee run through my bib shorts. It was really hot to feel the warm pee running into my crotch and down my legs. At first I started carefully but after a short moment I just let it run down my short without controlling it.
I don't think it was visible for others, I don't recall any steam rising from it, probably because at the same time the rain was running from my shirt onto and into my bibs. Still, it was very exciting to do this, and will certainly do it again when I have the chance!