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A non-Hermitian Weyl equation indispensably requires a three-dimensional (3D) real/synthetic space, and it is thereby perceived that a Weyl exceptional ring (WER) will not be present in thermal diffusion given its purely dissipative nature. Here, we report a recipe for establishing a 3D parameter space to imitate thermal spinor field. Two orthogonal pairs of spatiotemporally modulated advections are employed to serve as two synthetic parameter dimensions, in addition to the inherent dimension corresponding to heat exchanges. We first predict the existence of WER in our hybrid conduction–advection system and experimentally observe the WER thermal signatures verifying our theoretical prediction. When coupling two WERs of opposite topological charges, the system further exhibits surface-like and bulk topological states, manifested as stationary and continuously changing thermal processes, respectively, with good robustness. Our findings reveal the long-ignored topological nature in thermal diffusion and may empower distinct paradigms for general diffusion and dissipation controls.