Photonic devices are essential for high-frequency signal processing, notably in telecommunications. Emerging computational paradigms, such as Ising machines, benefit significantly from the high-speed capabilities of photonic technologies. Coherent Ising machines represent a promising approach to energy-efficient nonclassical computing, specifically by providing rapid solutions to combinatorial optimization problems. The temperature dependence of silicon’s optical properties presents a thermal design challenge for large-scale systems. We address this challenge by modeling the thermal behavior of silicon microring resonators to anticipate design constraints for coherent Ising machines. We used a 2D finite element model (FEM) mesh to model the cross-section of the waveguide that constitutes the microring resonator. The simulations were conducted using exclusively open-source software and demonstrate strong agreement with results from other research groups. The thermal relaxation exhibits a bi-exponential behavior, revealing a correlation between the widths of the silicon structure and the thermal relaxation times. Our results indicate that the thermal relaxation times can be varied by thirty percent using geometrical design parameters.