But the bottom line from my POV is that it in virtually all cases of a fire on board it would be impossible to be absolutely sure that the emergency is over.
The best and only course of action is to get on the ground. The degree of urgency will be dictated by the circumstances, but IMO in every case the landing should be done in such a manner as to not accrue unnecessary extra time in the air.
Another example from very recent history...a passenger seat started smoldering with visible smoke...after investigation, a cigarette lighter had been pushed in between the seat and seat back, and had ignited the seat lining. After the 'fire' was extinguished, the lighter was removed, and the seat was blocked off...should the crew have diverted? What if the only diversion field had no RFF? What if the diversion field had no ATC facility? Diversions may cost the airline hundreds of thousands of dollars, so they aren't undertaken lightly.
Safety First is a nice catch phrase, but if airlines TRULY put safety before the bottom line, they would rarely get airborne, and would certainly never make a profit. The MEL is a classic example...if safety was REALLY first, there would be no MEL...airliners would be fully serviceable, or would stay on the ground. It is all risk management. It is up to the crew to assess each situation on its merits, and use 'Airmanship' (the safe and EFFICIENT operation of the aircraft) to come up with a prudent course of action.
In the end, we have the comfort of another very important defence...the pilot has 'skin in the game'...if he is of sound mind, he will always want to save himself!