quote: "None of this makes sense. If the brakes were "hot" to begin with, then they should not have started the takeoff roll"
It makes sense, do you really think a captain would delay a flight because of hot brakes? I'm not talking about fuse plugs that are gone and warning lights that went off, that's indeed another story. You don't need OVERheated brakes to decide to let them hang in the air a few moments more.
There are even aircraft where a "hot" switch is installed that acts on the retract solenoid in the gear lever, to prevent gear retraction. Some kind of automatic system, the pilot selects up, but the aircraft negotiates when to do the gear up by itself.