I have had the same issue with my A6 (2009 4F2, engine CAHA) for more than 5 years ever since I bought the car and last winter the issue seems to have gotten worse. We have here nice frosty winters sometimes dropping to less than -25 celcius, in those temperatures the temp gauge doesn't even move unless I drive on motorway at high speed for more than 10 minutes. But even at a moderate 0 celcius the car is very slow to warm up and will not reach 90 on gauge unless on motorway.
I was considering replacing the main thermostat years ago but didn't do it because I just thought this is a diesel feature and forgot about it. Now I saw the fuel consumption is again high during winter and I became interested in this problem again. I found this topic which made me to do some more research and I think I have found an explanation.
The German engineers have decided to install an auxiliary water pump (called V178 in VW diagrams) whose job is to circulate coolant through the EGR cooler when the main thermostat is still closed. I found that this flow actually goes in reverse direction through the main radiator and goes back inside main coolant pipe into the EGR cooler. Then there is main coolant flow circulated by the engine pump which goes in many directions (straight to main thermostat, heater core and oil cooler). The flow through oil cooler goes back into the EGR cooler hoses, but it is blocked by the EGR thermostat. Now if the EGR thermostat 1K0121113A leaks too much, it apparently will let the warm coolant mix with the stone cold EGR coolant coming from the radiator. I am not 100% sure about it, but I think there
has to be a small leak through the EGR thermostat, otherwise it would never reach the opening temperature. But it is probably the issue that the EGR thermostat starts to leak too much or gets stuck open.
Then I figured that there must be an easy way to test this: disconnect the V178 pump (part number 19). I did this and bingo: it looks like engine temperature is now rising much faster and it seems to be more stable. I have only briefly tested it but I am pretty sure there is a difference. Of course it throws a fault code from disconnecting the pump but that is a small problem. So in my case the problem likely is the EGR thermostat.
Now many guys have stated that changing the EGR thermostat has not solved the problem for them. I also found this which is quite interesting:
https://www.clubtouareg.com/threads/dyi-egr-cooler-bypass-valve-actuator-repair.288901/
basically if the EGR cooler bypass valve is malfunctioning, it will start cooling the EGR gases right from startup which will rob the engine of its heat and cause the same symptoms. This is also easy to test: just see if the EGR bypass valve is moving when the engine is started. In my case it was working.