There was a recall in US for carbon built up.
'' Intermittently runs rough after coming to a stop with the engine at operating temperature.
Intermittently runs rough with engine misfires present after a cold soak startup.
If this condition occurs one or more of the Diagnostic Trouble Codes* (DTC's) P0300, P0301, P0302, P0303, P304, P305, and/or P0306 may be recorded
*The check engine light may illuminate for reasons unrelated to this condition. ''
The text above is from the recall letter. Might be worth doing a scan for errors.