We spoke to Safran Aircraft Engines (ex Safran), the aircraft engine manufacturer, who kindly gave us information for the CFM56 engine, the world's best-seller which notably equips the Boeing 737 and Airbus A320 families.
According to several passengers we asked, the answer to this question really isn’t easy. We’ll be revealing the answer at the end of this video. The figure is an impressive 1,750°F (the maximum tolerated temperature for these engines at takeoff) and around 1,470°F when cruising.
On the same topic, you can also watch the following video report on how does a jet engine work.