I have a 2002 Mazda Millenia which works perfectly. However, when it is cold there is a very loud thumping rattle which continues for several hours after start up-- As I drive and the car warms up the rattle diminishes – after driving for a few hours, the rattle is almost completely gone.
The noise might coming from a loose heat shield on the exhaust system. When these become loose, they can buzz, rattle, thump, and clank at certain engine operating conditions. As the exhaust system heats up and the metal parts expand, it can cause the loose heat shield to longer make any noise.
Bring the vehicle to closest muffler shop so the exhaust system doesn’t get too hot, and ask them to check for a loose heat shield.