There is nothing magic that happens at -40 with respect to the formation of condensation trails. Formation dependson several factors, and there are several forms which condensation trails (contrails) take or b which they are created. Relative humidity of the surrounding atmosphere is part of the factor, as well as outside air temperature. The internet is full of wild ideas about contrails, from the temperatures needed to form to irrelevant ideas about ram temperature rise, etc. The notion of -40 being any kind of pre-requisite, is equally nonsense.

-40 is generally considered the dividing line where all moisture in the atmosphere is frozen; water and precipitation no longer exists in liquid form below that temperature, in theory (For some time, that temperature was believed higher; I happen to know the individual who recorded water at -40, initially, in atmospheric research). What we knew yesterday, we know tomorrow, but differently, and so it goes.

I did for seeding in a former life; in low visibility conditions, we'd dispense powdered dry ice while flying at low altitude down a runway, preceding the arrival of a commercial aircraft on an instrument approach; this was done in low visibility conditions when the visibility was too low to legally accept the instrument approach. Visibility came up following our pass, allowing following aircraft to get in. This worked under specific conditions and was one of several methods in use; it was a type of "distrail," or dissipation trail, in this case an artificial introduction of condensation nuclei, or something for visible moisture to coalesce on and fall out of the air. Think of it as a lint roller for freezing fog.

Sometimes when we'd launch, flying twin piston airplanes, it was -15 degrees and crystal clear; the exhaust trail behind the airplane would create a fog that acted as a catalyst, and spread such that on the takeoff roll, a condensation trail formed behind the airplane, and slowly spread outward until the entire field was solid instrument conditions.

The first observed condensation trails formed behind piston airplanes at lower altitudes during the first world war. They were a common site by the time of the second world war, happening behind piston aircraft at altitudes much lower than 37,000' and temperatures much warmer than -40. In a standard atmosphere, -40 is reached by 28,000' but we know that standard seldom exists; it's often warmer, sometimes colder than standard, and given that -40 is not a magic number for contrail formation, it happens at lower altitudes, and often doesn't happen or happens intermittently at higher altitudes.

A lot of time and effort has gone into researching preventing the formation of both contrails and distrails, primarily with respect to military applications, as both provide clues to the presence of aircraft, visually. Contrail formation isn't always predictable, and it's very difficult to eliminate. On long flights behind other aircraft, we frequently see contrails stop and start as the temperature of relative humidity of a parcel of air changes (though relative humidity at high altitudes plays a minor role in contrail formation; temperature plays a more significant role.

Distrails can sometimes be seen in which the passage of aircraft through a cloud causes the cloud to disappear or appear "cut;" the cloud formation is dissipated by the aircraft passage.

For temperatures to be above -40 at 37,000 would be unusual.

Condensation trails form at warmer temperatures at lower altitudes, and are also a function of air density.