It is also possible that with climb thrust set, that stall induced turbulent airflow at the engine inlet(s) could cause a rapid rise in ITT exceeding the maximum limit. I am not familiar enough with the CF-34 engine control system to know whether it has a temperature limiting device capable of limiting a rapid ITT rise. I recall that it does have some kind of limited electronic engine control unit that takes effect at higher N1 speeds. Perhaps someone with the technical manuals could comment.
I have noted during my simulator training on two bizjet types that both of the major training providers teach the "firewall the levers" method for stall recovery and go-around/missed approach maneuvers. Unlike the real airplanes in the fleet, the sim will not overtemp/overspeed. In aircraft equipped with DEECs or FADECs, this will not harm the engines because the modern digital engine control will simply set max thrust very precisely while observing limits. However, on the aircraft I currently fly, this is a really bad idea. Very large exceedences are possible if you apply "radar power"! The older analog EECs do not anticipate limits. They do not act to limit ITT or RPM until after limits have been exceeded. During a rapid change of engine speed, the limits can easily be grossly exceeded just like they can on the purely hydro-mechanically controlled engines. I have mentioned this to the instructors and managers at the TCs. I was informed that this is the method they are required to teach. I don't know why. So I go with the flow at training and operate the real engines with greater care than they advocate. I guess it is another case of what looks good on paper versus the real world!
Best,
Westhawk