We are 
I don't know the exact numbers but it could be the heat of the smoke of the rocket (for the highest temperature) and when the rocket reaches the stratosphere (for lowest temperature). 
The most difficult thing for a launcher is to protect its passengers during a launch from turbulence and extreme temperatures. Do you know what those extremes are? #ArianeGroup #Ariane2pic.twitter.com/HmL1qefzqI
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Rocket Propulsion Elements by George Sutton is great!
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Basically, the hottest part of the engine , throat area. Where the mass flow rate is maximum.
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The throat
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maybe max Q for turbulence and highest friction during launch
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and the extreme cold from the propellant?
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