My M1 iMac can get noticibly quite warm around the bottom when I'm on a Zoom call with a lot of participants, or doing other intensive work like transcoding a video or something. I never audibly hear the fan, but I know it's running because warm/hot air is coming out of those bottom vents.
I haven't seen any sign of display anomalies, but fortunately I did extend my AppleCare recently so at least I'll have recourse if it goes bad.
Have you looked at Activity Monitor? My M3 is only getting hot there when the same 5-6 processes go crazy every day and I have to force quit them three times. I thought it's a Beta thing, but maybe it's more iMac related. It's not even warm if this isn't happening.
Looks like this and it happens without doing anything. Every time I looked for those when I not get warned by a menu bar app they all have 0.0% CPU usage.
