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