My air blows hot

It's possible you have a leak and all of the refrigerant has leaked out. You can try charging it yourself, recharge and leak fixing treatments aren't expensive at your auto parts store.

Check your heater control valves.

You simply need to go to your nearest repair shop, have them recharge the system (roughly $89.99 depending on your area). At that time they can determine if any of your A/C components need replaced. Hopefully it just needs a recharge though. Good luck.

There is no speedometer cable on the 2003 Yukon, if there is no transmission issues like shifting problem. Your instrument cluster has gone bad, to pinpoint. Your stepper motor to your speedometer gauge has failed and needs to be replaced. You can do a search on Ebay for the stepper motor for around $10.00 which is better then the $400.00 cost of another instrument cluster.
There was a TSB on the replacement of the instrument cluster for your Yukon free of charge. The only cost to you is the labor charge unless your willing to do the job your self. Just go to the Gm Dealer and give them this TSB Number: # 07187C: Special Coverage Adjustment - Instrument Panel Cluster Gauge Needle Function - (Mar 20, 2009)
Subject:
07187C -- SPECIAL COVERAGE ADJUSTMENT - INSTRUMENT PANEL CLUSTER GAUGE NEEDLE FUNCTION
Models:
2003-2004 CADILLAC ESCALADE, ESCALADE ESV, ESCALADE EXT
2005 CADILLAC ESCALADE, ESCALADE ESV, ESCALADE EXT (U.S. ONLY)
2003-2004 CHEVROLET AVALANCHE, SILVERADO, SUBURBAN, TAHOE
2005 CHEVROLET AVALANCHE, SILVERADO, SUBURBAN, TAHOE (U.S.ONLY)
2003-2004 GMC SIERRA, YUKON, YUKON XL
2005 GMC SIERRA, YUKON, YUKON XL (U.S. ONLY)
Some customers of all 2003-2004 model year and certain U.S. 2005 model year Cadillac Escalade, Escalade ESV, and Escalade EXT; Chevrolet Avalanche, Silverado, Suburban, and Tahoe; and GMC Sierra, Yukon, and Yukon XL vehicles have reported that one or more of the instrument panel (IP) cluster gauges stick, flutter, or become inoperative. This may cause inaccurate readings, including the speedometer and fuel gauge. Special Coverage Adjustment This special coverage covers the condition described above for a period of 7 years or 70,000 miles (110,000 km), whichever occurs first, from the date the vehicle was originally placed in service, regardless of ownership.
Dealers are to replace the instrument panel cluster after the condition has been verified. The repairs will be made at no charge to the customer.

For verified failures between 70,001 miles (110,001 km) and 80,000 miles (130,000 km) on U.S. vehicles, dealers are to provide the customer with an instrument panel cluster (IPC) only. Any additional costs, including labor to replace the instrument panel cluster, will be the responsibility of the customer. Dealers are responsible for the return of the customer's IPC back to the Electronic Service Center

Thank you for using fixya and good luck.

Check the fuses that control the climate control system. If they are in good shape check the vacuum lines that control the system. GM vehicles usually have a black ball that the vacuum lines go into somewhere under the hood to control the system start there and check al the lines and controllers.

I'm going to assume that is on both sides of the cab? I'm going to say you have an actuator problem, if it's in fact only blowing cold in the rear, and not in the front. The actuators are prone to problems on the gm product lines. Even more with a weak battery.

Its probably inside the dash, either in the coil or the connections

check you antifreeze level and make sure its full

I would try resetting both sides. i.e., Set both sides to hot, then back down to cool. Also check your fuse. I am not sure, but would think, you have a fuse for all these different items. It is time consumming, but look through and find your blown fuse. Hope it helps.

on GM vehicles they still use clutch fans and when sitting at an idle for a while the fan is not pulling enough air through the radiator and condensor so therefor the a/c starts to put out warmer air and the coolant temp. will rise a little bit. You could try replaceing the fan clucth and see if that helps any.