Grinding noise when starting car in winter

Okay so Corolla (2004 1.6 wagon) gives again new trouble. It is winter here where i live, and when temperature is below -0 celcius and corolla has been sitting whole night and you turn it on it starts to grind within a couple of minutes. Grinding comes from engine and it stops when engine gets warm and comes again only when you let it sit for hours so that engine really is cold. Oil is clear and its allmost at max. Coolant is allmost at max too. And when temperature is above 0 celcius there is no noise. And its not that kind of rattling noise what usually comes from bad chain. Suggestions?