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Serious diagnostic scanner you got there. It would seem that it's not possible for a cold sensor to read hot like that whilst sitting, or even upon startup, so the fault is either the sensor or perhaps pigtail connection to car and/or where sensor connects may be corrupted/bridged/grounded, etc. Always, always look for any background error messages stored, which may identify other related issues.
Hey, congrats on the TDI Q7! First thing you need to do is determine if the car has any TDI extended warranty benefits or not, as relates to the 'dieselgate' scandal. You can look it up online (Audi TDI Warranty) easily or contact a dealer near you. In America we have an extended warranty on the TDI cars they didn't send to the auto-recycler/crusher, which applies to the emissions and related systems, engine long-block assembly, turbo system and all sensors/piping, etc., and of course the the EGR, DPF and DEF systems. In short, most all things that could go bad or be impacted by the changes VW made to meet regulatory standards are covered.
The cranshaft pulley tends to corrode heavily and then falls off, quite literally. Be aware.