That's a hard call. I would rip chunks off my Nitto's every time out. I don't do as much tire spinning any more but my area has volcanic rock and granite. When i compare my street vehicle to my dirt vehicle, I tend to get more life out of my street tires.
Silt from sand and some dirt's leech the silicone out of the tire. This causes it to dry out and crack real quick. I haven't spent any time around clay so I can only comment on what I have out here.
I'm sure if its 120 degrees and your on asphalt, you can add that to your tire temp.