Seems that the throw-out bearing on a 2011 should have tens of thousands of miles left in it!
I doubt if warming up the engine would have anything to do with the noise being made by a throw-out bearing. I cannot come to think there would be a connection.
Does the sound change when you depress the clutch pedal? If so, it "could" be the throw-out bearing. But, it could be a short-lived DMF (Dual Mass Flywheel) if so equipped.
'84 Vanagon '02 ALH TDI engine(32 to 35+ MPGs consistently) Malone Stage 1 tune. Road trip to Nova Scotia 2013. Road trip to Alaska summer 2014 & 2016, 11k & 12k miles. 71k miles on install, Jetta Cluster odometer currently at 200kk miles.