I heard about the heating of the tires, but only on purpose and only in racing. Tires are sometimes heated on purpose by tire heaters or by simply making a lot of turns (zigzagging). The perfect example is Formula 1 racing. They always warm tires up because warm tires perform better and stick to the track more than cold rubber . These tires also have minimum curvature to have a bigger heat-radiating surface . Of course, there is a limit and tires can rupture due to the damage caused by deterioration, which increases when the rubber is warm. That's why they change tires so often. But the takeaway point is the better performance on higher temperatures.
Due to the above-mentioned, I think our greater enemy is the cold. I would rather use the veins to heat them. I am afraid additional cooling would lead to significantly reduced safety and increased rates of crashes. Yes, it would make the tire last longer, but at cost of safety.
The standard tire on an everyday car is manufactured to fight the heat for a couple of years of normal driving. You also have to check the depth of the curvature and the state of the tires once you drove a predefined distance. If you, on contrary, drive like in Fast&Furious, a regular check of tire condition is probably not foreign to you. So, the tire condition is your responsibility. Thus, poor condition of tires due to warming and deterioration of the rubber is the "necessary damage" we need to accept if we want a safe rubber tires.