Nice! I see you've already tried the standard technician's 'knock test' and 'twist test' for loose connections and dry joints on the PCB. Did you also try the last resort 'drop test'?
Possible problem apart from a failing screen is a dirty or improperly seated screen connection. My nuvi 40 screen flickered intermittently from new, so i opened it and spayed the connections with contact cleaner and reconnected. Problem went away. However, my 40 did that regardless of unit temp and was totally intermittent, unlike your 1440 flickering only when cold. That symptom would possibly be a dry joint 'making and breaking' when cold and making fully when hot and expanded slightly. Do you have another screen you can swap in to try if cleaning the contacts doesn't work?