I live within a stone's throw of a beach in the North of England. My partner, soon to be wife, first started running with just her sports bra on at Uni. After we started seeing each other we also became running partners.
My partner had encouraged me to try running shirtless for 4 months when on a very chilly October's morning she remarked on how schoolboy-like I looked by wearing a vest for a run and challenged me to take it off... a few seconds later off it came and I haven't worn a vest since.
We go out in all weathers, rain, snow and shine. Yes, people have looked at the pair of us out running on the beach but the only reaction we've had are people smiling and saying "You're mad!". Since we started running together there, are a few more runners, both male and female, out shirtless on the beach, including a group of teenage boys who are out running on most days too.
Some preliminary observations: We see, as has been alluded to elsewhere in this blog, that setting an example can cause others to strip to the waist. Also, the reaction from strangers is seldom to pour on vituperation, but is indifference at worst (shirtless in snow? no wonder some folks can't resist an exclamation). But what we also have here is a case of 'direct broaching of the subject' being what's needed to get someone to try something out.
The necessary cautionary note here is that one is probably best off never suggesting shirtlessness to anyone who isn't at the very least a semi-regular running partner. Though one may wish for the solidarity of a fellow-jogbraed or shirtless runner, broaching the subject could well be take in the wrong way. Run shirtless yourself: The possibility of thus 'inspiring someone else follow suit' is probably quite enough with someone you don't know fairly well.
Where the preconditions are met, though, some proselytising probably won't hurt. If your pal is obviously in great discomfort, gushing perspiration and such like, a kindly word that losing his top might mitigate things would be your good deed for the day. You might mention how your times have improved/ enjoyment level has risen/ mental wellbeing has surged since you took to shirtlessness. Take a leaf from Hoover's partner's book and frame it as a dare or challenge. If there's no reaction, let things be. You can always mention it again some other time: It appears Hoover's partner took four months effecting his 'conversion'. And she knew just how to pitch it too... but then again, she is to be his wife.
(I know of only one other runner who urged his running group to join him in trying out shirtlessness. Apparently, they would 'agree only some of the time'. This was a while ago, though, so perhaps by now barechestedness/jogbraedness has taken hold. If anyone else has a story - perhaps even a warning note to sound - to tell in this regard, do write in).