A parametric resonance due to temperature oscillations in superconducting micron-scale waveguides is considered. Oscillations of superconductor temperature are assumed to be induced by the irradiation of the waveguide with a laser beam. The laser power and parameters of the waveguide providing a possibility of parametric excitation have been calculated. It is shown that for a waveguide made of a YBa₂Cu₃O₇ microstrip with resonant frequency of 10 GHz a laser with a power of about 70 W/cm² is needed to excite oscillations. The effect can be used for the creation of high-sensitivity tuneable filters and optoelectric transformers on superconducting microstrips in the GHz range.