Sounds like urban legend (fighting legend?). The only two things that can be different are the weave and the material. Materials are pretty much going to be some blend of poly, lycra, spandex, and nylon. The weave isn't going to make a massive difference for heat retention, and it's easy enough to compare them side-by-side.
When I look at a surf rash guard and a grappling one, they look almost identical (modulo differences between brands). Hell, I'd bet most grappling rash guards are just sourced to Pakistani surf rash guard manufacturers and then sent off for embroidery/labeling.
And most, if not all, grappling rash guard companies aren't exactly big on R&D into material and fabric science or anything. If I was going to trust a company as having radically different designs for different conditions it would be one of the big ones like UA, Nike, RBK, Mizuno, etc. who can afford the R&D cost.
I mean, check this
crazy shit from Mizuno. If you're going to be rolling when it's cold, that's your hook up
And Mizuno has other stuff too like
this and they also use DuPont ColdMax on some of their gear.
And of course UA has their HeatGear and ColdGear stuff, which I use and love.
Nike also has some incredible stuff in the $40-50 range, which I can't link to since their site is all Flash. Grrr. But they basically have sweet long sleeve grappling tops, both loose and tight fitting, in a wide range of styles and colors and technologies.
Reebok has a
$25 long sleeve compression shirt as well.
I would guess that most of the compression shirts from the big name multisport companies are going to be higher overall quality than what you can get from a small fight wear company, simply due to R&D budgets and much larger testing base.
That said, support your fight gear companies and just hope their quality matches that of the big guys!
true MMA/Grappling rashguards vs. Surf rashies 
