Are you so sure about that...?
I shall give you some figures for the CJ610-6 (Learjet 24B).
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EGT temperature markings are "green arc" goes up to 702ºC
The "yellow arc" - 5 minutes operation (T/O) is 702ºC to 716ºC
EGT "red line" - 716ºC - 5 minutes T/O limitation.
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There is a second "red line" which is a momentary start limitation - at 950ºC
It is common to see EGT rising (fast) during start, generally to some 800ºC
FSI recommends to call it "hot start" if EGT continues rise beyond 850ºC
That is - within 100ºC of start "second red line".
Looks like hot start to all civilized pilots, except if familiar with these engines.
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According to my friends engine maintenance technicians -
Excessive start EGT is often due to HP bleed ports closing malfunctions.
That applies to the JT3D, JT8D and JT9D, engines I am most familiar with.
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A certain JT9D type might have a 950ºC EGT red line (Tt7).
A hot start is assumed if EGT rises rapidly above 500ºC.
For these type engines, a high FF is still the first clue of impending hot start.
Poor N1 or N2 acceleration (low bleed air start pressure) is the other clue.
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As usual - these are my classroom/simulator briefings.
If they are not as per "your SOPs" - just "fry your engines" as you wish.
Melted turbine blades are delicious, with a little Tabasco and salt.
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Happy contrails