Based on the bi-material triangle lattice cell, a new cellular structure, bi-material re-entrant triangle (BRT) cellular structure, is devised to incorporate tailorable coefficient of thermal expansion (CTE) and tunable Poisson's ratio (PR) properties by replacing the straight base of a triangle with two hypotenuse members. A general thermoelasticity equation to systematically build the relationship among the external force, the temperature load, and the deformation for planar lattice structures with bounded joints is derived and then embedded into a theoretical model for the devised BRT structure. Using assembled thermoelasticity equation, effective PR, Young's modulus, as well as CTE are computed. In order to guide designers to construct initial concepts, the design domain for coupling negative CTE and negative PR properties is plotted. The material-property-combination region that can be achieved by this cellular structure is determined within an Ashby material selection chart of CTE versus PR. Nine available combinations of CTE and PR properties are extracted and demonstrated with abaqus simulation.