Help - Fire Pit Question

I've been given an old John Deere 40" combine wheel from my cousin in MS. I'm in the process of building a 14' circular flagstone patio, with the wheel/firepit in the middle. My question is this: I want to wrap the wheel in stacked stone. The way the wheel sits on the ground, it's a bit concave from the bottom to the top of the wheel. If you can imagine a wheel without a tire on, it's not perfectly straight up and down, it's concave for the tube to sit in. My thought was to simply start stacking the stones, with the thought of having to "backfill" some of the concrete in the middle of the wheel, so the stones with be perfectly straight. Problem is, I think that wheel will get too hot, and the mortar will crack. Am I right here?? I'm new to masonry work, and need help please. My other thought was to start with firebrick on the outside of the wheel, then start stacking my rock on against the firebrick, instead of the wheel. I would rather not use firebrick, because that's just adding another step, and why use the wheel at all if I have to use brick. Hope I'm making sense here, hard to explain since I'm such a novice. Any help will be more than appreciated!!