Teemu,

When I was having cold starting problems, the relay under the hood was in the process of failing. The engine would take 3 to maybe 10 seconds of cranking to get it to start (where normally all you had to do was just think about touching the starter after the glow sequence and it would purr like a kitten) and then would emit massive clouds of grayish smoke which would make all the birds up in our tree scatter. Your description of it being okay when warm may indicate the relay is failing. There are two sets of contact points inside the relay. I'm no expert, but they appear to both operate together. Mine had pitting and burned surface area which, when cold apparently had too much separation to make contact. When it was warmer, this was not as much of a problem and it started much more like normal. If you pull this relay and open it up. You can see the points and perhaps see the problem.

You will have to scrape the silicone-like material from the bottom of the unit to see how to get it apart, but it comes apart fairly easily. The recessed nut/bolt that you can see when looking at the bottom is NOT the way to open it--been there, done that, didn't work. Check this out, it may be your difficulty.

Post back when you find the cause, okay?

Credit goes to Abe Crombie for this bit of information, since he is the one who told me about it and is tons smarter than me, which actually doesn't give you a very good idea of just how smart he is. :-)