Yoy would really have to look at what the engine is being told to do whilst on initial start up, It does things like stopping the water pump working until the cyl head gets to 70c, then starts the pump before again stopping it when the temp drops (infuriating on a cold morning when the screen is misting up)
They generally do things like advancing the exhaust cam timing and retarding the ignition timing plus as you have said maybe fully opening the wastegate, in fact anything they can do to heat the cats and OPF's up quicker. Audi are running scared after the last emisssion scandel, hence why the ecu is taking so long to crack