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Shape memory polymers (SMPs), classified as smart materials, have emerged as promising candidates for microfluidic devices due to their significant potential. In this study, we present the design and analysis of an SMP microvalve. The thermomechanical response of the SMP microvalve is studied using a recently introduced nonlinear constitutive model that incorporates nonlinear hyperelasticity and viscoelasticity for SMPs. This model is coupled with the fluid field and accounts for heat transfer in both fluid and solid physics. The governing equations for the multiphysics behavior are discussed. Then an overview of the finite element model is provided. The most important characteristics of the SMP valve, such as SMP thickness, flow rate, contact pressure, and pressure distribution, are examined numerically. The results expound upon the significance of employing fluid-solid interaction conjugated heat transfer analysis as a crucial factor in the proficient development of microvalves for diverse applications, with the primary objective being the prevention of overheating and the mitigation of potential failures. [Display omitted] • Fluid-Solid-Thermal analysis of thermally responsive shape memory polymer microvalve. • In-depth numerical examination of SMP valve characteristics. • The importance of multiphysics analysis in shape memory polymer microvalve design. [ABSTRACT FROM AUTHOR]