From our engineer, MQTW is based on maximum manual braking at touchdown with no reverse credit. The MQTW will change based on flap setting due to kinetic energy related to different approach speeds with different flap settings. This is a theoretical number because actual braking techniques are nothing like the assumed braking technique for MQTW. Also 30 note that the MQTW chart gives you a weight (the MQT weight), not a brake energy number. It you land above that weight, you need to cool.
Tactically speaking, if you exceed the weight with a flaps 30 landing, take a look at a flaps 40 MQTW. The flaps 40 will give you a higher MQTW which may be just enough to avoid the cooling requirement. This technique will not work at higher elevation airports where even a flaps 30 landing won't work because of Approach Climb, and you are forced into a flaps 15 landing.
The MQTW has nothing to do with the Reference Brake Energy, Adjusted Brake Energy, or Brake Cooling Times charts, which will approximate actual brake energy based on the braking technique used as opposed to MQTWs theoretical braking.
Regardless of what the Brake Cooling chart says in relation to ground or inflight gear down cooling times, if you exceed the MQTW, you are obligated to observe the MQTW cooling time. For our fleet, the -700 time is 62 minutes, the -800/MAX8 time is 48 minutes. The only relief allowed is that for a -700 with steel brakes. If the actual brake temperature measured between 10 and 15 minutes after landing is below 425F (218C) the MQTW cooling time may be waived. This provision does not apply to carbon brakes.