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A car in the Texas sun can get to be 180 inside. That's hot enough for the polymer chains to lose their unidirectional structure. If you live in most of the US you are fine, but I don't.
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I've studied this in great detail. And so have others; there's
a good paper on it here. As it turns out, the temperatures in parked cars are generally 20-30°C (36-54° F) higher than the ambient temperature.
The study above was done in Australia, where daytime temperatures peaked at around ~40°C, or 105°F. Temperatures in their car peaked at ~68°C or ~154.5°F.
It does not appear to be reasonable to expect temperatures of 180°F in any parked vehicle.
Having said all of that, the thermal stability of polyethylene-based armor materials has also been
studied extensively. As it turns out -- and this is a rare fortuitous coincidence -- they are completely stable below 70°C. And at temperatures slightly higher than 70°C, they're stable for up to seven hours. Temperature peaks in parked vehicles don't last quite that long.
So I don't think that you have much to worry about. Even on the very hottest Texas days.
If you are worried nevertheless, store your armor in the trunk of your vehicle. Temperatures in the trunk are not much higher than outdoor temperatures -- generally within about 10°C.