Rubber compounds harden with heat and age, traction can diminish rapidly when tires are overheated.
Now, consider this: I use a non-contact temperature gauge when our showteam travels, usually 7 towed boats/trailers.
Tire temperatures on our overloaded trailers are often 125 degrees when towing, I was amazed to find that a tire sitting in the sun could be 140 degrees, just sitting there.
I would never store a tire in the sun, a cold basement would be way better!