This is not only an issue with the 370z, but also the G series as well. Certain chemicals can cause issues with the dash long-term but also the windshield is working like a magnifying glass on sunny days and causing the dash to melt. I have the same issue happening on my G37.
Going forward, I'd recommend using a sun-shade, dash cover or tint the front windshield a clear ceramic film that blocks UV so it doesn't get worse.
It does suck.
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'08 Infiniti G37s - Forced Induction Fed
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