From the “Handbook of Construction Techniques” about in 1960
Keeping a Cool Head
After experiencing severe headaches for several days while wearing his metal safety helmet in the hot sun, Ray Vaught, a foreman with E. E. Barber & Sons of Texarkana, Ark., came up with a cool idea to take the heat off his head. He put a 1-ft-square piece of 3/16-in.-thick asbestos inside his helmet as an insulator.
The marked difference in temperature between a lined and unlined helmet was clearly evident by touch. By strapping a thermometer inside an asbestos-lined helmet, Ray found that the temperature inside was as much as 20 deg cooler than the temperature outside. It wasn’t long before everyone on the job had adopted his idea for keeping a cool head.
The guy's head is going to be roughly 100F, no matter what, so are we to assume that it was 120F outside on test day in Texarkana? (Doubtful, at best.) Yes,the surface temp of the helmet could hit that temp or hotter, but putting insulation in there would interfere with the evaporation of sweat that would provide some cooling.
If Ray was thinking the asbestos helped keep his head cooler it may be a symptom of having been out in the sun a few hours too long. ;-)
Having worn insulated (skiing & biking) safety helmets in a variety of conditions I can say with some certainty without empirical measurements that ventilation trumps insulation for keep your head cool in the hot sun, at any R-value (and that 3/16" asbestos was probably well-under R0.5.)