Computer modeling of rubbing between two surfaces with microasperities capable of expanding or contracting under conditions of frictional heating (i.e., possessing either positive and negative coefficient of thermal expansion (CTE)) allowed for the identification of wear-and-friction regimes on model ceramic materials. Assuming that no adhesion was involved in the interaction between asperities, two wear regimes—i.e., wear-free and continuous wear—have been revealed in both materials as dependent on the applied normal stress level and sliding velocity. The effect of the normal load on wear rate was similar for both positive and negative thermal expansion ceramics. Sliding velocity has a qualitatively different effect on the wear of materials with either positive or negative thermal expansion. The results indicated that the feasibility of reconstructing wear maps was common for both positive and negative CTE ceramics in terms of dimensionless mechanical and thermophysical characteristics.