They will take a compression set at high temperature. At higher heat they will shrink, harden and then crack. A rubber bellows can rupture. At cryogenic temperatures elastomers harden and stop sealing. The carbon A filler or binder can melt.
Blisters can form on the seal face as air trapped in the carbon expands because of the face heat.
Face pitting occurs when the blisters explode. Slip stick can cause chipping of the carbon outside diameter. The part can go out of flat due to differential expansion of the various cross sections. If the carbon was lapped at room temperature it can go out of flat at temperature extremes. The hard face Thermal cracking is common in some ceramics.