It has nothing to do with your fan,unless your fan is not cycling at all,its a mainboard issue!
Not to much you can do by stopping the console from overheating whilst downgrading!
You can try purchasing a internal fan mod,so when you first power on the console crank up the fan speed instantly yourself using the fan mod before the ps3 does it,this may keep the console powered on for a little longer...
OR...a cheap way is to reflow the console with the heat gun method ( presuming you don't want the console shipped to someone who reballs them ) and still have the fan mod installed when you re attempt the downgrade...
Otherwise your shear out of luck :-(