dumb cpu cooler mistake; possible overheating

basically got my mobo back from rma and decided to do a test boot to see if they really fixed it before i put the whole thing back together. one of the parts i omitted was the cpu cooler for my 7600x as i had heard somewhere that you could run with no cooler for a short period of time. i was gravely misinformed. is my 7600x cooked? it shut off on its own after about 30 seconds