Wavelength tunability of a microcavity solid-state dye laser is modeled by means of the finite element method. We investigate the application of two phenomena, thermoelastic expansion of the microcavity material and thermo-induced change of refractive index, in order to tune microcavity mode frequencies by the variation of the effective optical path. An optimized size of the laser microcavity is defined depending on the operation wavelength bandwidth and the glass temperature of the gain material.