Excellent color choice.
I too suspect your feeling it kick on and off. The compressor is the belt driven accessory that's right below your battery. Open the hood and see if it starts spinning at the same time you feel the thump. (turn defrost or ac on)
Now.. it should not be too big of a thump. There may be a possibiliy that something is wrong and yours is out of spec. If you think so.. take it back and have the service dept look at it.
btw, My 2006 FX4 WEB PAGE