One problem related to transmission solenoid has been reported for the 2010 Hyundai Sonata. The most recently reported issues are listed below. Please also check out the statistics and reliability analysis of the 2010 Hyundai Sonata based on all problems reported for the 2010 Sonata.
When vehicle is cold and I decelerate down thru 20 mph, the transmission down shifts abruptly causing a jerking motion. I have been told by an auto mechanic who researched it that there was an actual recall by Hyundai for this issue. He said the problem was that Hyundai installed computer control equipment from an older model in their 2010 Sonatas and this resulted in a failure in proper communication between the computer and the automatic transmission's solenoid, causing the abrupt down shifting at 20 mph when car is cold. One last note: when this first started occurring, it would cause the "fix engine" light to come on, but this has not happened for about the last three weeks. The abrupt down shifting when cold still occurs consistently, always right around 20 mph.