Planar optical waveguides consisting of layers from different materials created at elevated temperatures usually exhibit substantial stresses. These stresses are caused by thermal-induced strains that originate from the bonding of the layers in addition to intrinsic strains. For the first time, the analytical form of thermal stress formula is derived for the waveguide glass layer of the silicon-based silica waveguide in bilayer structures by the thin-film approximation and under the strain compatibility and the force equilibrium conditions. These conditions address the composite nature of the waveguide glass layer containing the waveguide core layer and the cladding layers within the optical planar waveguide. The developed formula reveals that temperature parameter, material parameters, and structural parameters affect the distribution of the thermal stress. By applying the formula, we demonstrate that it is possible to achieve the thermal stress-free, and, hence, the stress-induced birefringence-free waveguide devices by proper waveguide designs.