It's really difficult to say but logic would suggest that it's top end. . Gravity drags any oil back down to the sump so it's logical to assume that something isn't getting lubrication. Now i'm not too sure if the 1.9JTD 16v has hydraulic lifters, but if it does, then that sounds like the place I would start
Hydraulic lifters are charged up by the engine oil, they have a little hole that the oil gets into to pressurize the lifter. some usually remains inside the lifter ready for the next start up.
It sounds like the lifter/s are not getting this charge until the oil is warmed up and thin enough. Or the charge hole could be blocked by debris
You could try Forte additive lifter oil and see if that helps, it won't do any harm to the engine but worth a try.
Yessssss! Nero black, Black momo leather, sunroof and air con in a 156 2.0 twin spark..... = Heaven, pure heaven
Anyone can give advice on cars like "replace this part, replace that"... Start with the simplest solution and then work your way through it logically... Its a hell of a lot easier and cheaper!