It would be interesting to know a bit more of what flight profile is causing the alarm. My experience flying properly instrumented aircraft is limited to only two types so don't have general knowledge. However, in the two machines in question, with a bit of engine management you can get them to drop like a brick and still not get the shock cooling alert.
Something details like
Type -
Typical cruise - CHT, %power or rpm, EGT vs peak (or fuel flow), Speed
Descent - %power or RPM, EGT vs peak (or fuel flow), speed, descent rate, CHT cooling rate