Smokey, on the face of it your trainee is correct about the "thermal shock" aspect of his question. However (in my experience) that is probably not the reason for the cooldown procedure. Various engines have required a similar procedure, and it probably is related to compressor efficiency during startup. (If you induce a starting stall/overtemp, that's quite a "thermal shock", ain't it?)
Some engines also have tailwind limits for start (early JT9D-3's were notorious for this), while others have no such limits. Some require waiting till 15% N2 or greater before fuel on, others are happy at 10%. DC-10's had derated APU's for many years, but the CF6's seemed to start just fine at low pneumatic pressures.
In short - the 93°C limit was likely determined empirically or statistically to give the least probability of a hot start.