sputter at 1300 to 1600 rpm

[6.2L Driver]

I just picked up a 1998 6.5 turbo diesel 135,000km. It seems to run and accelerate smooth when it is cold but in warm weather above 0 degrees C and the engine is warm on an easy slow acceleration it sputters though 1300 to about 1600 rpm and as a result feels rough. Also it smokes a blue smoke not a black smoke like on a hard acceleration. On a hard fast acceleration there seems to be no rought range. I have changed the fuel filter and air filter is also new. Also in park or neutral and i just step the petal to the floor quick it has a rough spot too, not a smooth rev up and down. What could be wrong with my truck? I am new to the turbo diesel, all my experience is with my 1982 6.2. With this 1998 there seems to be a lot of black smoke if I let the truck shift a gear up and it is kind of lugging, or when i dont accelerate fast, could there be a problem with the turbo spooling up?

[rjschoolcraft]

May be lot's of things going on at once. Your black smoke issue is likely boost related. Check the wastegate solenoid and vacuum pump/system. Do a search here and you'll find hours of reading on these subjects and how to check them.

I'd correct this issue before chasing the stumble... it might just go away.