Why did the light come on? Why did it extinguish?
It is worth remembering that the loop detecting the WHEEL WELL FIRE is a single loop installed int the wheel well itself, triggering an activating of the light at a predetermined temperature, extinguishing the light at a predetermined temperature.
Thus, it may well be that the gear extension has caused the 'hot' parts (if located not the landing gear assembly) to be now located in an airflow sufficient to extinguish the potential fire and/or cool down the hot parts causing the activation of the light.
Furthermore the removal of these hot parts from the vicinity of the loop will cause the loop to reach the predetermined minimum temperature soon and the resultant will be that the light will be extinguish.
Thus the statement from the Boeing Memo as supplied here bears truth.
Should however there be a fire located not on the extended landing gear assembly, the loop continues to sense the fire temperature range and remains on. This would be an indication to the crew that the fire is indeed in the wheel well and not part of the landing gear assembly. Reasons for this could be plentiful, the described hydraulic incident in previous posts being one such reason.
It cannot be emphasised that the loop is a temperature detection loop only and its location is not on the landing gear but inside the wheel well itself.
Given the fact that the crew came from an airport where IDLE landings are often achieved by said operator and brakes are not often subsequently released to cool the heat stack ons stand, with no evidence of fire or excessive heat after the landing, it may be wise to look at the aircraft's history prior to the incident and to not just look at OFDM data from the flight but of the flight arriving prior in PMI. Furthermore as OFDM does not capture ground events after shutting down engines, this may be our only clue to possible hot brakes which may have required cooling to take place.
PS: In PMI 24L is not commonly used for departures, which sounds a bit odd in the initial post of the incident. For landing 24L it provides a rapid exit S1 which can be especially useful for aircraft parking North of the terminal to vacate, but this requires a very short landing distance to be achieved and consequently a high use of brake forces to achieve it, especially with common tailwinds on that approach resting in higher ground speeds on touchdown. Reversers have little effect when LDA is so short due to the deceleration rate of the aircraft and spool-up time of the engines to reach reverse thrust level of >70%.