My thoughts, it takes 30 minutes to appear gives the impression it's heat related. I would start right from where the exhaust pipes leave the engine compartment and inspect each connecting point,especially the heat shields.
Catalytic converters will rattle once they warm up IF the ceramics have broken loose.(rare).
My 08 Jeep had such a problem, drove me crazy, only after it warmed up. Believed it was converter. Took it to a muffler shop, where the pipes crossed over there was a metal skid plate, it had a broken weld. Why only when it was warm was a stumper even for the muffler expert.
My guess is it's the shields. Get a mirror and a flashlight and get under there OR get a shop to inspect on a lift.That's money well spent.
