In regard to exhaust temps........
I have an additional module installed in my Golf R32. It provides a myriad of temps, g-forces, torque etc from (approximately) 200+ sensor locations around the vehicle/engine, that are identified/interrogated by the ECU/CANBUS system.
Interesting to note, that exhaust temps are recorded in at least 2 areas along the journey from exhaust manifold to the exhaust outlets themselves. I have seen temps of 750C+ from one of the sensors during a session of WOT. When you de-accelerate the temp drops immediately, so I understand that the temp readings are pretty accurate.
Point of my post is that the exhaust specialists are probably quite correct, and certainly, the closer to the engine that you (can) take the exhaust temps, the higher they will be. However, the air (exhaust) temp does drop quite noticeably closer to exit, and of course once dissipation to the atmosphere begins.