2002 gmc yukon denali rough idle, low idle about 500 rpms on cold starts or when air is turned on

Check for trouble codes. You can get this done free at most car part stores.

should be mounted on the side of the throttle body

Fuel pressure regulator will fix it.

Check for vacuum leak at intake or plenumn while it is cold , also check temp sensor. i have done a few intake manifold gaskets on these vehicles.

add freon it is low

have the low side pressure cycling switch tested.

Here is a TSB (Technical Service Bulletin) for your vehicle for loss of temp control.
File In Section: 01 - HVAC
Bulletin No.: 01-01-39-007
TECHNICAL
Subject:
Loss Of HVAC System Mode and/or Temperature Control 

(Reroute Wiring Harness)
Models
1999-2002 Chevrolet and GMC C/K Pickup Models (Silverado and Sierra) 1999-2002 Chevrolet and GMC C/K Utility Models (Avalanche, Suburban, Tahoe, Yukon, Yukon XL, Denali) 2001 GMC Sierra C3
2002 GMC Sierra Denali
2002 Cadillac Escalade, Escalade EXT
Some customers may comment that they cannot control the HVAC system modes and/or the temperature. These concerns may be intermittent.
Cause
There may be poor terminal contact and/or bent terminals in connectors C206 (RPO C68 automatic HVAC controls) or C296 (RPO C60 manual HVAC controls). Excessive tension on the wires due to the wiring harness being miss routed in the instrument panel carrier may cause these conditions.

If the warranty campaign is over i am sure they can or may have in the system on how to correct the problem.
Good luck and hope this helps, keep me posted if you need help on to the repair procedure.

try to get a scan code . it may be the throttle sensor or a number of things.they san for free at AutoZone.

i now for a fact that it is the egr valve . carbon balls in side you have to take it of and clean them out

Most sensors will trigger the check engine light, however the TPS(throttle position sensor) or EGR Valve(exhuast gas recirculation valve) could be potential causes. Does this problem only occur at idle? Is the idle normal in park? Let me know and I can try to assit further.

Hope this helps