Remove the graphics card and CPU heatsink if its large, then lay it down sideways in the car. Then just make sure it wont slide around while driving and you should be fine.
Wouldn't the video card and cpu heatsink be fine if you lay the case down on a seat? Its not a very bumpy ride. If I take out the heatsink wont It mess up the thermal paste? (Its a CM Hyper 212+)