In fields such as flexible electronics and aerospace engineering, where dimensional accuracy demands precise control of thermal deformation, mechanical metamaterials with tunable thermal expansion properties are gaining significant attention. These materials enable thermal expansion matching with surrounding components, ensuring high thermo-mechanical stability under temperature variations. This paper presents the design and analysis of a metamaterial capable of achieving tunable coefficients of thermal expansion (CTE), including positive, zero and negative thermal expansion, through internal bending deformation. A pseudo-rigid-body model is developed to establish a theoretical thermo-mechanical performance model, which is verified by finite element analysis (FEA). The proposed model was employed to conduct parametric analysis on the metamaterial, elucidating the correlation between structural parameters and effective thermomechanical properties, while simultaneously establishing a novel modeling methodology applicable to other mechanical metamaterials. Both theoretical and FEA results demonstrate the capability of the proposed metamaterials to serve as structural or functional components in engineering systems for avoiding undesired thermal expansion mismatch.