Re: I'm not an expert
Very true, but that's only used after the engine is properly ignited and running under its own power, plus the really hot bit will be just behind the aircraft anyway when in use.
A hot start is generally when excess fuel is ignited at too-low a level of RPM so that the turbine blades in the hot section of the turbine exceed their safe operating temperature - even transiently.
Since the blades in the hot section are usually operating close to their melting/deformation point even when everything is working OK (and only don't melt due to clever cooling holes), a temperature excursion will lead to a hot section inspection being required at the very least to see if any of these blades have deformed/fused
If it has done a reverse flaming fart up its own jacksey like this which needed extinguishing (as opposed to an over-temperature tell-tale warning), then they will probably need to strip it down to get rid of the extinguishant out of the turbine anyway.