They will heat up very quickly without a fan. However, the P4s have built-in thermal protection, which will throttle down the CPU speed so that it doesn't overheat too much. THG did a thing a couple of years ago, showing P4 vs Athlon vs P3, and they removed the HSF, and showed Q3 on the screen, and it slowed right down to just a few FPS with the P4.
You really shouldn't run it without the fan working though.
Confused