Purdy,
Thanks for your thoughts on this. I'm inclined to think the muffler warming after shutdown is mostly an old wive's tale (although I never heard wives talk about such things). However, I agree with your original thought that an exhaust manifold crack or connection leak is the most likely culprit. That would explain the delay in backfire--as the system cools down, air will be drawn in thru the crack creating the right mix for an explosion. This might also require (1) that the car be running too hot, which could be from either retarded timing or too lean mixture or dragging brakes or ..., and (2) an excess of unburned fuel in the exhaust, which could come from either running too lean (accompanied by misfiring) or too rich (accompanied by smoke and dirty plugs.
The exhaust system heating up after shutdown just doesn't make sense to me; how could a cooling exhaust system draw in air thru a manifold crack if it's actually heating up??
Steve