Barring any sort of progress via the above suggestions, it's possible for the Engine Temperature (ET) sensor to be stuck at a warm reading within operating parameters even when it's rather frosty outside. I've known a motorcycle or two that has displayed similar symptoms (barely start cold, then run prime when warm) and had a sticky ET. There should be a fairly simple test with an ohmmeter provided somebody has the temperature/resistance scale (I'd look into this for you, but kiatechinfo.com doesn't want to talk to me today).

www.wellsmfgcorp.com/pdf/Counterpoint2_2.pdf
This links to a pdf article about ET sensors, at the top of page 3 there is a fairly simple test, remember to keep the key off any time the sensor is disconnected or the CEL will likely be on more frequently than before.
Good luck.