A3 1.9 TDi SE 2002 blowing cold air but with a normal 90c running temp

She`s away for the weekend so she had a longer trip yesterday and she found that the temp only starts to creep up when she accelerates harder to overtake ( not every time though ) she thinks its when the turbo kicked in I do know for certain it has had a new turbo fitted so I should be able to rule out that and the reader didn't throw up any codes for that so hopefully you guys are right with your first ideas and the stat is either faulty or maybe stuck so just thought id let you know the the latest things she has found out in case it points to something different all together ill try get hold of a thermostat on Monday but I may have to wait until Tuesday depends whether TMS have one in stock speak later thanks.

Wondering if anyone could help me. I've recently had a new water pump and belt fitted because my a3 1.9tdi losing water. Upon replacement, it then broke down cause of a switch on the big black pipe feeding to radiator. Was replaced and also system bled (as original mechanic didn't do)

The problem I still have is that the car gets up to temp eventually running down the motorway for instance. Then upon slowing/idle the blowers start blowing cold again - in this time also, the temp gauge is up at 90 and blowing cold. Then tends to drop back to about 50/60/70.