I am surprised it is not standard practice and also not even a self start or a start warning based on warm up time of even a particular engine on given temp conditionings.
It could also be programed further on the many factors available today. What is the worst case at a busy port? wait at holding for another aircraft to land if by chance you are not "warm" or if very close an extra 10 second line up (with warning).
It would certainly same lots of fossil fuel over a year.