The recent development in the field of microparticle acoutophoresis in microsystems has led to an increased need for more accurate theoretical predections for the acoustic radiation force on a single microparticle in an ultrasonic standing wave. Increasingly detailed analytical solutions of this specific problem can be found in the literature [Settnes ans Bruus, Phys. Rev. E 85, 016327 (2012), and references therein], but none have included the complete contribution from thermoviscous effects. Here, we solve this problem numerically by applying a finite-element method to solve directly the mass (continuity), momentum (Navier-Stokes), and energy conservation equations using perturbation theory to second order in the imposed time-harmonic ultrasound field. In a two-stage calculation, we first solve the first-order equations resolving the thermoviscous boundary layer surrounding the microparticle and with a perfectly-matched layer as a non-reflecting boundary condition for the scattered waves. These first-order solutions are then used as source-terms for solving the time-averaged second-order equations [Muller et al., Lab Chip 12, 4617 (2012)] and in particular to determine the second-order time-averaged hydrodynamic stress on the particle surface. From this we deduce the radiation force and compare it as a function of the physical parameters to existing analytical results.