Airliners have brake temperature indications of some sort. On the one I fly, green is good, amber(yellow is bad). If it’s in the amber then take off is prohibited, would not be enough brake energy in case of a rejected take off. I have had hot brakes right about to go amber and I always left the gear down an extra 30-60 seconds after take off(assuming there are no obstacles I needed to worry about). If the brake heat becomes excessive it could result in a fire. There are safeties designed into the tires that will cause them to deflated if they reach a certain temp, instead of exploding. The issue with your flight seems like they had retracted the gear into the wheel well and the enclosed space exacerbated the issue. To compound the problem the fuel tank is usually just inches above the wheel. So it was prudent for them to extend the gear for a few moments to mitigate the risk. In my experience I’ve had great support from ATC, if not I ask for priority handling. If that doesn’t work I’ve had to declare an emergency and then I have the airspace and ATC haS to move everyone out of the way.