There are difference of opinions about "land at nearest suitable" and "land ASAP."
Feet dangling, fire indicator still on, ASAP, light out, nearest suitable?
On the 737 and, I believe the 57 and 67, wheel well fire detectors are single loop. The engines and APU utilize more reliable dual loops. I've been told Airbus tends not to have wheel well loops at all, relying on brake temp sensors instead.
It is ironic to think that following TEM procedures would increase the hazard, RAT 5! I can think of alternate CRM scenario with your silver haired gent saying: "Ignore it sprog, I've seen it xx times in my career and they all turned out to be duds."
If the overheat detection was due to a fire on the wheel assembly, when it is lowered the heat source is removed from the detection loop, thus extinguishes, but will the fire be out on the extended undercarriage?
200+ knot airflow should take care of a rubber-fueled fire, but if the fire is fueled by Skydrol, or worse, magnesium, all bets are off.