Have a look on AKS tuning, it lists both the BWA and the K04 engine cars stats.
https://www.akstuning.co.uk/shop/home/1069-genuine-tfsi-inline-thermostat-4e0121113.html
Mines up to temp in around 3 miles, no harm trying the easiest option first but I would be surprised if it made any difference, it always seems to be the main thermostat that fails.