Engine noise and jolt when starting

I have a 2008 MDX with 43K miles and been experiencing a problem when the engine starts. For the most part, the engine starts smoothly without any problems. But sometimes it seems that the engine hesitates for a split of second before it actually fires up. When this happens, I can feel a slight jolt from the engine compartment. Occasionally this problem is accompanied by a loud "bang" noise. I noticed this usually happens when I start the car after it cools down for an hour.

The car is out of general warranty but still under power train warranty. The dealership said it will cost $180 for diagnostic.

Any suggestions will be appreciated.