In summary, remember that the cessation of the wheel well fire
warning does not guarantee that the fire is extinguished.
It plainly says/suggests to plan to land at nearest suitable airport - which they then did.
The above are quotes from 2 previous responses. In the former, taken from a Boeing memo, this does not appear in any Boeing pilot issued document that I have see, While it might be good airmanship this advice is somewhat hidden. Equally I've not been aware of the concept that a wheel well fire warning was associated primarily with hot brakes. I've had such a false warning in a phase of flight where it was nigh impossible to have come from hot brakes. We mdd an immediate return to field of departure; taking about 15 mins from a medium FL. The QRH procedure did extinguish the light. I discussed with the F/O the possibility of a combined hydraulic leak (fine spray) and an electrical spark. No way of knowing. What I didn't appreciate was that an extinguished light might not be honest.
In the 2nd one the 'land at nearest suitable…' in various companies and sim scenarios has never been emphasised as ASAP. When I did have various fire warnings, then extinguished, in sim scenarios, and elected to land ASAP, I was chastised for not going through the 20 minute stage play of QRH, CRM, NITS, Ops call, PA, set up FMC, brief, etc. etc; even though we had just taken off from a base airfield with OK weather. A spin round the circuit was heresy.
I think Boeing should do better to clarify and inform crews just what these sensors are telling them, or not, and to outline just what is expected of the crew. The response from T.C's in various airlines was interesting if confusing. What was good airmanship in one was forbidden in another.
Having said that, in one LOFT with the latter type airline, with an inextinguishable engine fire after takeoff it was deemed sensible to rip it around and down ASAP: much to the amazement of the SFO who wondered what the hell I was doing.
From what the Boeing memo says, i.e. a WW fire warning extinguished does not mean the fire is out = should mean on the ground ASAP and NOT holding to burn off fuel. Crews do not seem to appreciate this.