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Do you have a simple code reader that will check for malfunction codes that may be set in the Engine Control computer? Can you get me an audio clip of the noise under the hood when this happens on your phone and post a link here?
Noises are very difficult to diagnose in this type of format unless I can hear it. Any chance you can record that on your cell phone and post a link here? Does the noise seem to happen while it's idling and if you push on the accelerator does the noise go away after a minute or two?
Any chance you would be able to get a recording of the noise to me? Otherwise I can give you a couple of ideas but it's purely conjecture without hearing the noise.
Okay based on your description and the time and occurrence that it happens the most probable cause is due to very slight cylinder misfire. On this engine when that happens it causes a severe clunking or knocking sound especially at idle. If you raise the engine RPM very quickly by depressing the throttle pedal all the way to the floor anthe noise goes away and it smooths out then you have a issue with slight cylinder misfire. This can be caused by multiple things sparkplugs possible water contamination underneath of the ignition coils or even a defective ignition coil. Without having a code reader to at least find out what the basic malfunction codes are in the Engine Control computer its difficult to say for sure if the car runs fairly well can you get to a nearby auto parts store like Autozone or similar where in most states except California they do free malfunction code reads. Any generic code reader will work to check the engine computer to see if there any cylinder misfire codes.