My teenage son (13) is self conscious about body hair, how can I help him?

I'm sure it's just normal growing pains, although I'm aware a lot of younger (and reasonably older it seems) generations are into removal of body hair (personally I don't get it) this seems a little excessive.
Right now I'm happy that he told me, but the situation is such that he won't wear shorts when in school at the gym or when we do training together. He must be absolutely dying with the heat.
I've tried to get him to wear shorts, told him to look at eveyone else in the gym - they all wear shorts and the vast majority of the guys have hairy legs.
He's insisting on wearing track suit bottoms at all times in the gym.
I pointed out that this is a normal part of becoming a man, I asked him if kids were slagging him at school or anything, he says no, but I'm not sure.
He's a confident enough kid otherwise.
I'm not sure how I can reassure him more, he usually loves wearing shorts and sandles during the summer, now I'm worried he's going to insist on wearing track suit bottoms the whole time.
How can I help him? Do I need to?
Any thoughts appreciated.