NB: 36,000 feet in 3 minutes is 12,000 feet/min. Max climb rate for the Lightning was 50,000 feet/min, but it got there by basically pumping fuel into the afterburners with a fire hose.

(The Lightning had two main defects as an air defense interceptor: insane fuel burn rate at max thrust, and limited armament. The longest ever recorded sortie without in-flight refueling was 1h56m, but it was common for them to be running low on gas and need to tank up 20 minutes after a hot scramble.)