See https://www.youtube.com/video/X3PhjpWxedQ?ecver=2
How to repair cracked brick in a front-loading kiln. First remove the damaged brick using a drill and chisel to route out and remove brick. Then shape a cut firebrick piece to fit in the space and cement in place. Then sand. Let the cement dry overnight and then do a slow bisque firing to cone 5. This same technique can be used on kiln bottoms and in other situations like on the side or back. Hi-Temp kiln cement can be used instead of phosphate bonded cement (which is no longer available).