When you have high residual ITT from a previous flight, it is always good practice to let the engine crank to the limit of the starter motor's capability before introducing fuel. If it will go to 20% Nh, let it get there before introducing fuel; if it won't crank past 15%, too bad, run it to its time limit then put the fuel in.
Or consider a 'dry motor' first to pull the ITT down, let the starter cool off for a couple of minutes, then start. Don't worry about reducing starter motor life by such abuse. Starters go for a long time, so if you reduce one's life by say 100 hours it won't be much in dollars per hour. However engine hot section overhauls are much more expensive if the engine suffers too many hot starts or has to be removed before its TBO.