Rough Idle in Drive/Reverse & Park only when warm

What is your question?

My car starts fine. Idles great until fully warm. Car will idle rough, shudder, etc only when warm or when rpm's drop under 1,000. I have had 3 mechanics thoroughly look at the car and everything checks out. I have been told that it is possible that the motor and transmission mounts are bad. Could this be only at a low idle as the symptoms are not there when cold and RPM's of 1,000 or higher, either when cold or when I increase speed in park. Sometimes worse then other times. Some people have told me that worn or bad motor mounts will cause a vibration all the time and not just at idle. Some mechanics also want to replace the throttle body/idle speed motor, which is quite expensive. There are no check engine lights, no stored codes, idle speed, fuel trims, MAF sensor readings, and pretty much everything else checks out with a scanner. The car is a 2006 Corolla with 89,000 on the odometer. One owner and a lot of city driving. I am the second owner.

What makes this problem better or worse?

Problem exists only when warm, not cold

How long has your 2006 Toyota Corolla had this problem?

Since purchase of vehicle, and has become worse