Finite element analysis is used to explore composites of negative thermal expansion materials with positive thermal expansion materials (ZrW2O8 in Cu and ZrO2 in ZrW2O8) and evaluate how thermal and mechanical properties, rates of cooling/heating, and geometry and packing fraction influence the overall expansion and thermal stress. During rapid temperature changes, the transient short-time thermal expansion can be considerably larger than the steady-state value. Furthermore, thermal stress in the composite can be large, especially at the interface between the materials, and can exceed the material strength.