According to my copy of AP3340, the Handbook of Aviation Meteorology, contrails are likely to be visible when condensed water or ice particles are present in sufficient concentration to be seen. This in turn depends upon illumination, background contrast and distance.
For the formation of a contrail, the air temperature needs to be below a critical value which varies almost linearly from about -24 degrees celsius at sea level to about -45 deg C at 50,000 feet.
The critical temperatures are indicated by a particular line drawn on Metform 2810, the tephigram. This line is marked: "MINTRA," and will apply to an aircraft flying at cruising speed in an atmosphere just saturated with respect to ice. The corresponding temperatures for saturation with respect to water are lower by about two or three degrees C.
Trails may form at any altitude provided that the temperature is suitable. At 1000 millibars the critical temperature is about -30 deg C, so trails can occur at ground level in high latitudes!! Over southern England the average altitude at which trails would be expected to form in the winter ranges from about 26,000 feet to 70,000 feet. In summer, when the stratosphere is warmer, the range is about 30,000 to 45,000 feet.
So on the tephigram, a MINTRA would be that temperature above which a trail will not form even if the ambient air is already saturated. And a DRYTRA would be a line joining temperatures at which trails must occur even if the ambient air is completely dry. Between these two limits, corresponding with saturation and complete dryness, trail formation may be expected to depend primarily on the relative humidity of the environment and, to some extent, engine thrust.
On the Kipper Fleet in the 1980s, each sortie saw a specific briefing to the whole crew by the duty meteorologist. Such luxury, eh?
No doubt, for you in Transport, it can't have been too much different. Anyway, a tephigram could, and probably would have been specifically prepared for the types of sortie to which you allude in your post.
I hope this helps!
Regards,
Dai Farr