@Nitpicker330:
I think Piper19 was telling that the crew took off with brakes below the maximum temperature of 300°, but that there is a possibility to get a BRAKES HOT warning after TO because the brake temperature can rise due to the closed compartment of the gear.
Not all A320 have brake fans to cool the brakes.
Let's say that you take-off with a brake temperature of 290° and you have a short flight. When you land it could be that the temperature is still around 290° and you have to land on a short runway with MLW and OAT is around 40°C.
No brake fan available for cooling. Good luck in trying to cool the brakes before the next flight.
Delaying retraction or an early gear extension can reduce the time you have to wait on the ground. Brake fans can be very useful, if installed, because with certain conditions it's very difficult to cool the brakes on an A320 if you don't have them.
Just saying that with the right conditions and no brake fans, the brakes can use some help to cool down. I've been in this situation before.
About having an engine failure with the gear extended, ofcourse you'll need to retract the gear as soon as possible.
But with an engine failure at V1, initially your gear will be extended as well.
And with an engine failure after V1 you will already have gained more altitude on the initial climb with 2 engines and gear down compared to an engine failure at V1