I have one that did almost the same thing. I noticed that it ran better in warm weather and really bad it cold weather. It ran better with the choke on part way. If I could get it running fast it ran better. I replaced the pilot jet with one 3 sizes bigger. If it is affected by temperature it is most likely fuel related and most common is too small a jet. I also bought a new carb. ended up with the old carb and bigger jet.