This sounds very much like Fletcher. Although he is only 10, he's had arthritis for about 4 years, and it has gotten bad in his back end in the last year or so, and the panting has been almost constant, especially in the summer. What has helped him has been acupuncture and Chinese herbs. He has been on this for about a month, and is doing much better. He also still takes rimadyl and tramadol.
I think the panting is a combination of pain (better with the addition of the Chinese herbs), allergies (will start on that next), heat (turned down the AC), and stress.
If acupuncture is available in your area, I would strongly suggest you give it a try. It can't hurt, and has made such a difference for us. I was lucky enough to find a mobile vet who comes to the house