so it's impossible to shock cool a turbine? or the FADEC or FMS is taking care of that, which will prevent it?
I have never seen a limitation on a turbine related to shock cooling, but I won't yet venture to declare it "impossible"... However, I cannot recall any any such warning for any turbine engine I've flown with -- FADEC or not.
Limitations I've seen pertain to heat-soaking the turbine (e.g., run at idle for X minutes after running at high power, before shutdown).