Recent advances in Neural Radiance Fields (NeRFs) and 3D Gaussian Splatting (3DGS) have achieved considerable performance in RGB scene reconstruction. However, multi-modal rendering that incorporates thermal infrared imagery remains largely underexplored. Existing approaches tend to neglect distinctive thermal characteristics, such as heat conduction and the Lambertian property. In this study, we introduce MrGS, a multi-modal radiance field based on 3DGS that simultaneously reconstructs both RGB and thermal 3D scenes. Specifically, MrGS derives RGB- and thermal-related information from a single appearance feature through orthogonal feature extraction and employs view-dependent or view-independent embedding strategies depending on the degree of Lambertian reflectance exhibited by each modality. Furthermore, we leverage two physics-based principles to effectively model thermal-domain phenomena. First, we integrate Fourier's law of heat conduction prior to alpha blending to model intensity interpolation caused by thermal conduction between neighboring Gaussians. Second, we apply the Stefan-Boltzmann law and the inverse-square law to formulate a depth-aware thermal radiation map that imposes additional geometric constraints on thermal rendering. Experimental results demonstrate that the proposed MrGS achieves high-fidelity RGB-T scene reconstruction while reducing the number of Gaussians.