[ Post Update: This is not an F3 Issue as suspected. If you get this same error and you've altered your fan settings or not, my advice is to check your fan settings via FSD or DashLaunch, check the side of the xbox to see if air is blowing out as well as other troubleshooting steps ]
I changed the speed of my fan on my Xbox 360 s (Trinity) to 70% a few days back, then after powering off the console going back onto F3 and changed it back to Auto. Its quite possible that F3 may have saved a setting somewhere where the fan speed changed be from 70 to 0.
When I powered the xbox on, the fan did not come on, at all. I've no idea what caused this, i deleted F3, reinstalled, no fix, so I just flashed the dashboard again and that fixed it.
Of course, I didnt see the fan didnt come on, so took it off, instaleld new thermal paste then after powering up the console with the case open I noticed the fan didn't spin.
Not sure if this glitch was on F3 or other but if you change your fan speed, keep an eye on the temp.