Running hot and smoky - turbo at fault?

[juz22]

I've noticed rising coolant temps over the past 3 days, at first it went to 93 then today to 96-97.
Prior to that it always sat between 85-90 solid. Was fitted with a new head gasket and water pump about 15k miles ago. Also had a second hand turbo fitted at the same time but this wasn't reconditioned. Radiator and heater matrix are both reasonably new. It has a Bosch with t2 turned up to 16psi.

The rad gets hot and the coolant level is fine, but I changed the thermostat today just in case that was the problem, but it hasn't fixed it.

I noticed a few weeks ago a bit of blue smoke on cold start but it cleared quickly so I wasn't unduly concerned. Today it was very very smokey at idle which clears under low load driving but on heavy acceleration there are bigger plumes of smoke than normal.

I tried driving off boost but temp remains at 96-97, doesn't come down on idle. Fan kicked in once today but I haven't heard it come on very much.

Could this be my turbo leaking oil into the inlet, and would that cause the coolant temp to rise by so much compared to normal? Or is there something else I'm missing?

[juz22]

Additionally I noticed today after a completely cold start the temp went straight to 80 within seconds of starting the engine, whereas normally it would take 5 mins before it would even register movement from 70. There's no way it could have stayed this hot whilst switched off. Is that likely a faulty temp sensor, or can something genuinely make it get that hot that quickly? The only thing I can think would be water pump failure but that's is only 15k miles old so shouldn't be disintegrating?!