Overheating 2.0T FSI

[sram]

Hi all
A Happy New Year to all forum members.

My 2006 petrol Avant has recently started overheating. I have scanned with VCDS and nothing out of the ordinary regarding engine or cooling was revealed. The temperature sensor circuits match what's displayed on the dash and VCDS.
The heating works fine and there is coolant in the expansion tank.
The temperature will climb to between 100 and just under 130 degrees after driving for about 15 minutes. If I slow down and take it really steadily then the temperature will come back down to 90 and slowly start to climb again once speed picks up.
I did suspect the thermostat being stuck closed but I'm not so sure as the main radiator top pipe is warm when the car overheats, so I believe this shows that water is flowing around the system? I have not yet removed the front grill to have a good feel of the radiator.
If anyone has any further suggestions it would be greatly appreciated. Of course, this chooses to happen out of the blue just after having to purchase a new washer-dryer after Christmas

Thanks all

[inspectorman63]

Most thermostats have a bleed hole so some hot water will get past. Or it may have failed slightly open. Your diagnosis is probably correct and it's cheap enough to start there. But when was your water pump last changed?

[sram]

I believe the water pump was done in 2016 along with the 'toothed belt', according to the service book. Is there an easy way to check the function of the water pump?

I bought one of those infrared thermometers today and got the car up to an indicated 120 degrees. I pointed the gun at the radiator and it said it was 5 degrees all over. I pointed it at the large main hose coming off of the thermostat housing and it said it was 51 degrees. Does this help with a diagnosis?
If I knew which pipe was the thermostat bypass pipe, I could also point the thermometer at that as it should be much hotter than the main pipe (am I right here?).

Off to search for a schematic of the BPJ engine.