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Minimization of dissipative losses is a major goal in microelectromechanical systems (MEMS) resonator design. For an accurate simulation of a MEMS resonator vibrating in a vacuum, thermoelastic damping phenomena related to irreversible heat dissipation induced by the coupling between heat transfer and strain rate during resonator vibration and acoustic radiation into the substrate have to be taken into account. The finite-element method (FEM) is suitable for structural simulation, particularly for thermoelastically damped structures vibrating in a vacuum. When the vibrating structure is deposited on an unbounded elastic medium, radiating conditions have to be taken into account. The boundary-element method (BEM) is suitable for simulation on an unbounded medium, and it is often used to complete the FEM. The goal of our paper is to develop and to validate a thermal-electromechanical FEM-BEM tool, which is helpful to predict and understand MEMS energy loss dissipation mechanisms.