The N1 carrot shouldn't stay put anywhere on the climb. It should start somewhere in the neighborhood of 89% N1 (at climb setting) at sea level to about 97% N1 at 37000 feet. The way I undestand is that the FMS computes target N1 based on temperature and altitude. I also don't think it is trying to maintain a constant value of anything on the climb out, but follows a schedule programmed into it that Bombardier determined to be optimal, although around 800 degrees ITT seems to follow the schedule pretty close, but not exactly. My guess on the ITT fluctuation in the climb is that the FMS does not take into account actual pressure at altitude. So, if the pressure is lower than standard I would expect to see a higher ITT for a given N1 following the climb schedule, and vice versa for higher pressure. Just my observations, please chime in with others.......