This car has an disturbing noise like someone hitting the right rear quarter panel with their fist. It is spasmatic and cant be duplicated with effort.A thorough check of the chassis while up on a hoist found nothing wrong.It seems to happen when the engine is not up to temp -it happened last when it was pulled into the garage[not moving] maybe one to three times on a short local trip.

 

Which engine do you have? The noise could be the exhaust banging on the tunnel side, or even the axle cage. If nothing else seems obvious, might be worth loosening the clamps front and back of the axle cage and carefully re-aligning the exhaust.
Just had another thought, test that the shocker bolts at the top of each unit are tight, and that the bottom pin is also tight.
Greg

 

bbaum, When you locate the noise culprit, please post how it was corrected. I have the same issue with my 93 XJS coupe.
Mert

 

Maybe the body in the boot wasn't dead after all lol.
Sorry couldn't help myself.