This certainly sounds like a problem which only exists when the engine isn't up to operating temperature. While it could well be that the piston rings are expanding with the temperature and finally sealing properly, because they are so hard to check, I'd consider several easier checks first.
If the smoke is white or whitish gray and accompanied by a bit (or more than a bit) of an oil slick, you might check your pre-heat system. Some engines continue to operate the heat system for a few minutes after starting. If the pre-heat/post-heat system isn't working, the engine may nevertheless start (especially in the mild weather around here) but fail to consume all of the diesel that's injected until such time as the cylinders warm up to operating temperature. In that case, the slick isn't really "oil", it's unburned fuel. If you've got an electronically controlled engine, diagnosing heater failure can be tough. If you don't, it may be as simple as checking the electrical power to the heater elements. I don't know if you have glow plugs or possibly a "toaster", but if you can isolate the leads you can at least see if they are getting power. Of course, they may also be burned out, in which case an amperage draw check may be in order--again, tougher to do, but possible.
If the smoke is blue or blue/gray (and if that's what you mean by "oil smoke") consider your oil consumption. If you're burning oil, you do have a problem. I'd maybe start by just looking at the turbo if you can see it with the air cleaner off (engine stopped and turbine fully wound down, of course.) If it looks clean and moves freely, move on--not because you've eliminated the turbo as a problem, but because it's passed one easy preliminary check. Unless you're approaching normal rebuild hours for your engine or you've overheated it, I'd leave the piston rings for later. Next, I'd check the valve stem seals if I felt comfortable getting this involved (I wouldn't with someone else's engine, but I might with my own.) Beyond that, I'm on the phone to a mechanic.
BTG