Cold start over fueling smoke ?

[Simon quatt]

Hi am a proud owner of my 2004 Audi 2.5 tdi 8E5 b6 Quattro avant love it, however I have been struggling with a problem that I really need to sort,  on cold start in winter boy does it over fuel a lot of diesel smoke which does clear, hence not in the summer when the ambient temperature is up a little I guess, I tried locating the fuel temperature sender but couldn’t find it, I gather my model has it in the injection pump itself not sure, I can’t seem to find help with this and it’s been going on for too long and throwing money at the diagnosis with specialist people too, I would love to hear from someone please and will appreciate your input thanks Simon quatt.