A turbine engine experiences a lot more "shock" during the engine start than any transitions in flight, be it cruise to idle on a descent, a missed approach power increase, or otherwise. In fact, it's harder on a turbine engine to shut it down without a normalization period, than to make power transitions.
As a mechanic (engineer, to some), I've handled burner cans that looked like shattered swiss cheese. You might be surprised at the amount of damage that's normal in a turbine engine burner can. Damage such as cutting and burning on turbine inlet guide vanes, blade creep, rubbing, etc, are all bigger issues on rotational parts. Turbine engine parts are air cooled, even with an influx of fuel (with a power increase), a proportionately greater influx of cooling airflow takes place. Even in the burner can, where a layer of air normally prevents flame contact with the can walls.
The single greatest thermal shock to an engine occurs during engine start, of course...but this isn't a shock. The only thermal damage we're concerned with is overtemperature...which can damage blade coatings and blades, damage the metalurgy, cause streaking (raw fuel downstream from the nozzles, which causes spot burns right through the cans or burns on the inlet guide vanes or turbine blades...or torching with nozzle damage), etc. Thermal damage can occur during a compressor stall in which the temperature may rise substantially higher in the can (and even reverse flow to some degree, as expanding, burning gasses tend to stop moving aft and expand in both directions) or sections forward of the can...but not immediately register on EGT or ITT gauges (because the fire is going on somewhere other than the temperature probes). That's also part of the reason for start limits which are lower than takeoff limits, incidentally; it's two-fold. The internal temps aren't turbonormalized yet...so the limits are lower. Additionally, the temps going on inside the engine may be higher initially than what you're seeing on the gauges until the engine is stabilized and on-speed...it gives you margin. In any case, that's where your greatest thermal threat lies.
So far as pushing the power up manually and "shocking" the engine, don't forget, it's self heating, and it's continuously normalizing itself (preheating,if you will), so it's ready when you push the power in.
A turbine engine is full of dissimiliar metal; it expands at inconsistant rates, and it cools at inconsistant rates. During normal operation everything is preheated and kept that way, all the parts function as a team. After shutdown, if the engine isn't given a brief period to normalize (or to get fairly uniform temperatures throughout), then certainly the rates at which some parts continue to increase in temperature (some do, after shutdown, believe it or not) and others begin to rapidly cool can cause siezure or rubbing or other problems...part of the reason that many manufacturers provide a minimum idle run time prior to shutdown (often two or four minutes).
Anyone who's ever run a Garrett TPE-331 and had to spin the blades by hand after landing, or who's experienced shaft bow due to the temperature differentials gets the idea.