Apple iMac 24-inch (M4) runs hot or the fan is loud

The checks in more detail

Nektony's guide adds that a Mac on a soft surface or pushed against a wall cannot breathe, so place the iMac on a flat, hard surface with space behind and around it. The iMac's vents are at the top rear, and a monitor arm or a shelf above it that blocks the vent holds heat in. Dust enters over the years and clogs the fan, and a can of compressed air blown into the vent in short bursts, with the Mac off, removes some.

Warm rooms and direct sun raise temperatures. If the fan is loud while Activity Monitor shows little CPU use, a sensor fault or a failing fan is possible, and Apple Diagnostics, run by holding the power button at start-up and choosing Diagnostics, tests the fan and sensors and gives a reference code. After heavy work such as rendering video, the fan runs for several minutes to cool down, which is normal. Update macOS, since thermal tweaks arrive in updates. Check for apps that stay active in the background, such as cloud sync clients re-uploading a large library.

A Mac that shuts down from heat, or a fan that grinds or clicks, needs Apple Support. Do not open an iMac; the glued display makes it a job for a technician. Place a small thermometer or use a free sensor app to check temperatures, but remember that the iMac's case being warm is normal, and what matters is whether the fan stays loud at idle. If the fan is loud only while a particular app runs, update or replace that app. Keep the room at a normal temperature, and avoid covering the vent with papers or a speaker on top.