Where is the horn relay on a 2008 tahoe - 2000 Chevrolet Tahoe

If you used a jumper wire on load side of horn relay and the horn sounded, the horn itself isn't the problem. Have you checked applicable fuses? Not only check the fuse, check for voltage on fuse circuit, use a testlight.
The horn button on the steering wheel and associated wiring is ground for control side of horn relay.

One way to find out for sure would be to pull the relay and jump 30 to 87 where the relay plugs into . Good horn operation ,relay is bad , Just because you hear clicking doesn't mean the relay is good . VEHICLE RELAYS Operation Diagnosis watch this on relay testing .

The horn button is bad may be part of airbag$$$$

Someone would need to test the relay and the circuits it controls.
The horn pad grounds the relay to make the horn blow.

First off take the horn pad off the steering wheel be careful if has air bag ground your self with a wire so know static lift pad off disconnect the wire see if horn stops if so the horn pad might be collapsed and letting it make a ground this will set horn off

the temp is fine 186 would be too cool for this engine. as far as the horn it could be the horn contact in steering wheel a relay,blown fuse, bad hoern. the relay and fuse for horn are underhood in the power distribution box. it will have a diagram on inside of cover check the fuse if it is good. hold your hand on relay while someone pushes horn if it clicks relay and contact are good and it is horn itself. if no click swap relay with another like it in box still no click probably the contact in wheel.

This is a challenging repair but you can do it yourself if you are comfortable with the following instructions. For tools, you will need a voltmeter, a set of allen wrench screw drivers and a set of wrenches. The horn on a Chevy Tahoe operates with the use of a relay. This means that the power for the horn is received from the fuse block under the hood. Power from the fuse block runs to the horn relay. The commonly open end of the wire goes to the horn. The horn is then grounded to the frame. Power to the activating terminal of the relay comes from the Body Ride Control or from the accessory side of the ignition switch. The negative side of the relay runs through the column to the clockspring. The clockspring is also used for the air bag system. The wire then continues to the steering wheel air bag where it is attached. As the air bag is pressed, it causes the wire to ground, actuating the relay which, in turn, activates the horn.

For a step by step set of instructions on how to proceed go here
http://www.ehow.com/how_6003439_troubleshoot-horn-chevy-tahoe.html

J.

here is a link to the wiring schmatics. The horn circuit is on page 27. http://www.pswired.com/misc/pacaudio/syswire.pdf

You can remove the horn relay and use a Ohm meter and check the resistance between the horn relay connector terminal No. 86 (Black Wire) and ground. If the ohms are less then 5 ohms replace the horn relay. There are a lot more tests but as Polarcycle states you can do what he suggested other then I believe you have two horns in this vehicle.

If you can locate and pull relay, do that, if not, pull wires off at horn if you can, otherwise pull fuse. If you have other relays same in area of horn relay (same number on relay) try one of them in that horn spot to see if maybe it's just a stuck relay.If you pull fuse for horn, you may find out something else on same fuse, so make sure you check everything else is working.