Structurally optimized lattices have gained significant attention since the commercialization of additive manufacturing (AM). These lattices, which can be categorized as metamaterials, are used in aviation and aerospace industries due to their capacity to perform well under extreme structural, thermal, or acoustic loading conditions. This research focuses on the design of a unit cell of a multi-material lattice structure using topology optimization to be manufactured using multi-material additive manufacturing processes. The algorithm combined with octant symmetry and support elimination filters yields optimized unit cells with overall reduction in effective coefficient of thermal expansion and thermal conductivity with high mechanical strength. Such unit cells can be used in multi-material additive manufacturing to generate lattice structures with optimized structural and thermal properties.