Having not seen anything offered from the medical community members, I thought I'd chime in here.
As mentioned in the abstract of "Heat Stress in Motorsports...", the sentence is: "The Body's primary thermoregulatory pathway is sudation (the process of sweating and evaporative heat loss)." We tend to forget that saturated clothing (driver's suits) will not evaporate fluid from the skin surface, since the skin is not exposed to air. Only the wet suit is. Point being that we forget to get out of the suit when coming off the track, and put it out to dry...don't wear it. Better still, find a dry suit to wear the next time on track.
Cool suits will help to remove heat, no argument here. Staying out of the sun, AC, fountains, swiming pools, etc, will also. These periods at the track are when a crew (person) is valuable to your health...doing the work between sessions to enable the driver to cool off.
Hydration should begin at least two days before the event, and continue thru the event, with at least two days after the event to help replenish the body. Don't forget glucose, sodium and chloride with the water replacement. That salty taste to your skin means you are losing them also when you sweat.
Sorry to have to mention this, but, try to eliminate alcohol and caffine from the diet during the hydration schedule, as they are diuretics...they will help the body to eliminate water (going in the wrong direction here).
Combinations of methods will work also...cool suit, prolonged hydration schedules, cooling devices directly to the body, proper evaporation and cooling after the event. Above all, be alert to the symptoms of Heat Stroke (life threatening), and Heat exhaustion (performance degradation), and be ready to act accordingly when the symptoms occur.
Guys, it's just like racing in the rain (a different type of racing), where you have to have different equipment, and follow a few different rules. It's surviveable.