I acknowledged that this could still be true in my comment, but that I would have to actually do some analysis. However, what the parent comment said is wrong. Your gas is going to lose internal energy to shaft work as it moves through the turbine, which then compresses the inlet air.

Not saying its not hot or hotter, I'm saying the air is not moving through a compressor (which /would/ heat the gas as it does work on the gas to move it to higher pressure), it moving through a turbine, which is recapturing the internal energy of the exhaust gas to improve the efficiency of the engine.

Because this site always needs ""SOURCES"" https://www.theturboforums.com/info/article/why-are-exhaust-...

>EGTs are usually measured close to the head. This provides a much quicker response time as well as a more accurate reading. In fact, the temperature of the exhaust gas following the turbocharger can be as much as 200 to 300 degrees lower than the temperature upstream of the turbo. Air resistance caused by the turbo itself can also cause increases in the temperature upstream that would not be detected past the turbo.