Net undergarments have been used off and on since WWII. It was popularized by Collin Fletcher (The Complete Walker) The idea was that worn under a windproof layer, the net trapped air and provided insulation. Allowed to breathe, it would provide evaporative cooling. Warming and cooling in one garment... Kalu, Kalay.
Unfortunately, the original cotton net had all the disadvantages of cotton. In addition, the net would emboss your shoulders under the pack straps leaving you with a neat pattern of blood blisters, bruises and abrasions. The solution was to make the shoulder and yoke from regular jersey knit. I've still got one of those. I think they stopped making them around 1975.
Brynje makes cotton and polypro mesh underwear. Their claim that the polypro products won't absorb water is probably accurate. I don't have any of their stuff, so I can't say if the mesh is deep enough to do the jobs of both warming and cooling. The opinion current with the older products was that the mesh should be at least 3/32 of an inch deep and preferably closer to 1/16" to function properly. I see that Brynje's tops are all mesh. Therefore, I suspect they are likely to be uncomfortable under pack straps.