1998 Jeep Cherokee starting car

When my car starts up it will idle fine for about a minute. After a moment it starts idling rough for about 4 or 5 minutes. This happens irregardless of the weather. It then "clears up" and I can pull out and go. If I do not wait to go through this process the car will not accept gas while I go down the road. The car wants to hesitate and has no pick-up. I have had this problem for about 2 years and it is getting worse with time. No warning light has ever come on to tell me what the problem might be. I have brought the car to two different garages. Both have run diagnostic tests and have not found the problem. Do you know what may be causing this? Is this a common problem with Jeep Cherokees? Any input would be greatly appreciated.