Wavelength tunability of a microcavity solid-state dye laser is modeled by the finite element method (FEM). We investigate the combination of thermoelastic expansion and thermo-optic effects to tune the microcavity resonant wavelength. An optimized size of the laser microcavity is defined depending on the operation wavelength bandwidth and the glass temperature of the gain material. We also report a new effect of mode depletion specific to our microcavity and excitation scheme.