Brainy people will tell you how hot jet exhaust condenses the moisture in the air to make contrails but just how hot and how cold are we talking about?
This picture is from 34,000 feet. The contrail ahead is the path of another jet's climb to level flight at 36,000. The first thing to think about is being a kid. Thats right, on the playground in the cold playing with your mouth open watching your breath drift off in misty haze and disappear. Thats just like jet engine exhaust but to create gigantic trails like this we need a huge ammount of heat to find and condense the very scarce and limited moisture from the thin air. How hot?
In cruise at 34,000 feet we saw an outside air temperature of about -51 Celsius (-60f). The engine exhaust temperature we indicated was 770 celcius (nearly 1500f). Thats a temperature difference of, well, I cant divide -60 by +1400. Its huge. Now, were burning basicly 11gallons of kerosene a minute as well so the expansion of hot gasses out the compressing tailpipe at 1400 degrese creates something like a blowtorch as big as your car.
Those are the forces at play.
Picture credit is mine. (No contrails were found or harmed during this article)