Exhaust noise rattling

Check the exhaust system from front to rear for torn or warn hangers, welds broken on any shields. That is if the noise is a metal noise or rattle. Please describe your noise if this doesn't match.

Under the car like the exhaust? Catalytic converters do that inside their metal shell or housing. Beat on it with your fist when it is cold to hear it. (Not running).

Sounds like you may have a exhaust loose or either the cat converter is stopping up. Some of these have baffles inside which will break loose and cause a rattling noise. When the engine is cold, start the vehicle and crawl under and hold the converter with your hand and even the exhaust to see if any pressure will stop the or alter the noise. Careful it don't take long for the exhaust to heat up. If these baffles are broke inside, it can cause the converter to become stopped up and rattle, this will also give an engine false info when it comes to the fuel and air ratio mixture. Not going to far into it, so i don't confuse you. Good Luck

Have a look at the shrouds around your exhaust system, they are prone to shaking loose and rattle on over run.
Try giving your exhaust a bang ( with your hand when it is cold) and see if it causes the noise . Follow the noise.
Sometimes the baffles fall off inside the muffler and rattle around inside too.
Happy hunting!!

4.0l's are notorious for valve rattle on cold start-up. There is really nothing you can do to make it go away short of completely replacing the valve train in the top end, and that isn't a permanent fix. It's is an top end oiling issue from the factory. Just don't race your engine on cold start-up until the rattle stops.

The rattle in the transmission sounds to me to be more of a loose dust shield/heat shield around the transmission or exhaust than a mechanical issue.

chek exhaust system mufflers , catalytic convertor. When car is COLD take a rubber mallet and smack these items. Listen for the rattling noise. Hope this helps

Check the heat shields on the exhaust system. They get loose from the extreme heat fluctuations work loose and rattle. Especially the one between the engine and firewall where the 02 sensor screws in. It probably rattles less after warm up because heat causes expansion which makes it tighter. Hope this helps.

When the engine is cold, go under the car and try to shake the exhaust system at the approximate spot you hear the rattle coming from. It is most likely a heat shield for the exhaust, or a broken (rusted through) hanger for the exhaust making the noise you describe. You can probably correct it with a wire or couple of screws to secure the shield, or replace a hanger.

This only happens when the Car is Cold???? It is the Exhaust Manifold. You need to Replace the Exhaust Manifold Gasket and check the Rest for Tightness.

Try checking the heat shields on the exhaust pipe up front under the car. Alot of times they will loosen up, and begin to rattle. You can ither remove them, or try to clamp them.
Hope this helps!