Abstract: Heat dissipation from the surrounding rock at excavation roadway is an axisymmetric heat transfer problem. Accurate determination of the rock temperature field and the unstable heat transfer number is a prerequisite for airflow temperature prediction. Control volumes for the finite volume method were constructed by centroid-based partitioning of triangular elements. The dimensionless axisymmetric heat conduction integral equation for the surrounding rock was discretized accurately using area coordinate functions. A dedicated solver for the rock temperature field at excavation roadway was developed on the Visual Studio platform. The effects of the Biot number and Peclet number on the temperature field distribution and unstable heat transfer number were investigated, and mathematical models for the unstable heat transfer number were established for both the heading face and the surrounding roadway. Results show that the cooling range is smaller near the heading face, whereas a larger cooling range develops in the surrounding roadway farther from the face. Increasing the Biot number reduces rock temperature near the wall and enlarges the cooling range; increasing the Peclet number raises rock temperature near the wall and shrinks the cooling range. The unstable heat transfer number for both the heading face and the surrounding roadway increase with increasing Biot and Peclet numbers. In the surrounding roadway, the unstable heat transfer number is maximal near the heading face and decreases with distance from the heading face, with progressively diminishing spatial variation. Based on the computed unstable heat transfer number, corresponding mathematical models were formulated and an engineering application procedure was provided. For a representative set of field parameters, the model predictions agree well with numerical simulations, with a relative error of 0.10% for the heading face and a mean relative error of 3.52% for the surrounding roadway, confirming the model accuracy. Moreover, the proposed models are concise and computationally efficient, eliminating cumbersome chart/table lookups and facilitating subsequent calculation of roadway airflow temperature.