Pancho, on the old manuals 737 classic (the only ones I have for the moment), the QRH drills just refer to the Fire Warning Light ,
not to the OVHT light.
Anyway, I believe now both lights will be illuminated.
I agree with Menen when he raises the point that continuing the takeoff with an OVHT implies the risk of having a fire JUST BEFORE V1.
You assume that the fire wrng will come only in the air, and you'll have time to manage it.
But actually, the fire wrng could come just before V1, and you'll have to abort at high speed, and we all know the dangers af aborting close to V1.
That's one of those matters where it's impossible to find absolute truth....
Probably the best solution is to select the lowest V1 possible on short/slippery runways... V1 wet minus 10, as David Davies suggests in Handling the big jets.
....
The master wrng light and the fire bell are inhibited after V1 till 400 ft or 25 seconds, which frst, on the 747/400.
LEM