In this work, we analyze and design structures and materials that possess custom thermal expansion. These structures and materials are composed of a base unit inspired by the tensegrity “D-bar” (or double-pyramid) topology. We derive, for the first time, analytical equations for the linearized and geometrically exact coefficients of thermal expansion (CTEs) of bi-material D-bar structures with arbitrary shape and complexity. Numerical results obtained using the geometrically exact CTE equations are compared with results obtained using the linearized CTE equations, showing that the latter are accurate only in cases where temperature changes are small. Further results show that D-bar structures of low complexity can produce a wide range of CTEs, including positive, zero, and negative values. These CTE values are exhibited for a range of materials that allows for easy manufacturing (materials with CTE ratios as low as 2). Thus, it is concluded that D-bar structures show promise for applications in aerospace engineering and other fields where new materials of tailorable thermal expansion are needed to decrease the substantial thermal stresses caused by large temperature changes.