Hi,
just to be curious: What is the temperature when you find the starting trouble?
I have used my Sore in conditions below minus 30 Celsius degrees (yes, last week here was -34° Celsius, and this I can say is cold). When starting from scratch it takes some seconds to cough and blue smoke is coming from exhaust pipe. But after 5 to 10 seconds engine is idling smoothly (or so smoothly it can in such coldness) again. This is normal behaviour for diesels, I have owned different brands from Land Rovers and Nissans to VWs and Mercedes, and every one acts about similarly.
I have heard some comments from Kia drivers here about CRDIs: We are using extra engine heaters here (working with electricity or with vehicles´s own fuel). When you are starting the pre-heated engine, some sensors may give faulty signals to control box and this causes rattling and unstable idle after annoying starting. When pressing down the gas pedal nothing happens, only the engine attempts to stop.
This may take minute or two, then all is normal again. Explanation is that control box thinks the temperature is quite warm, but as a matter of fact incoming air is freezing cold. It takes a while to adust the settings again.
Mainly these comments have come from Sportage drivers with 2,0 CRDi.
I don´t know if there are differences in Kia´s equipment geographically delivered. But I am sure if the problem you described is a feature, people here has noticed it and complained strongly.
I think one of the first things you can ask your service to do is to measure the glows. They have specific resistance when they are ok. If one or more plugs are dead (resistance immeasurable) or out of specs, the symptoms are like yours. The engine starts rigidly when cold. After warmed it runs ok (I have experience of this).