Okay, so we've done a little bit of research and I think I might've hit on not one, but two PvP fire builds. The first up is the old POM Pyro build and the second is a deep fire version. Without further ado, here we go.
Ye gods and goddesses. This is a potential PvP arcane/ fire hybrid. The idea behind this build is to give us the quick "Execute" and increase our longevity against the opponents who wish to outlast instead of execute. What I did was give clearcasting, Presence of Mind and Combustion to stack with our Blast Wave, Pyroblast and Scorch. It should go without saying that you won't cast Pyro without Presence of Mind. Pyro is your execute move. After you put Scorch and Fire Blast on them (with Combustion), you need all the crit you can get to overcome the resilience your opponents have.
This next one is a deeper fire spec. No Presence of Mind here. In this build, you can see we've gone deeper into the Fire tree for our 41 point talent. It's horrendously inefficient, but it's another stun effect. Essentially that will be your bread and butter. Once again Combustion to help our crit chance and loads of stuns. Hopefully you'll be able to overwhelm the resilience and any stun resist abilities/ trinkets they carry. You need to go in full- bore and get your win in the first 30 seconds or so or you will be in a world of hurt.
There we go. A couple of (hopefully) Arena- worthy fire specs. Give it a go and have fun.
Edit: Curse my eager clicking. The second spec now has all the points assigned...