A cooler is not a cast iron cooling rack.

No.

Tossing a screaming-hot cast iron pan into a cooler seems like a clever shortcut, but it’s a bad idea. Coolers are designed to keep things cold, not to handle direct heat. The interior plastic can warp or melt, and the sudden temperature difference can cause the pan itself to crack from thermal shock.

Even if the cooler survives, you’re trapping steam inside. That moisture will condense on the pan and cause rust, and the trapped heat will just make the cooler hot instead of cooling the pan efficiently. You’re better off letting the pan cool on a trivet or a cold burner. If you’re in a hurry, set it on a heat-proof surface and walk away for ten minutes.

Your cooler is for beer, not for blacksmithing.