Abstract: Heat release from surrounding rock is the dominant heat source in deep high-temperature mines, and its key parameter—the unsteady heat-transfer dimensionless number K_uτ—directly determines the accuracy of air-temperature prediction. Existing methods for obtaining K_uτ (analytical series, charts, tables, piecewise regressions, or case-by-case numerical simulations) are either computationally cumbersome, suffer from large interpolation errors, or cannot be implemented in batches, thus failing to meet engineering demands for rapid, accurate and unified calculations. To address the above issues, a study on the calculation method of the unsteady heat-transfer dimensionless number between roadway surrounding rock and airflow has been carried out. Taking a circular roadway as the research object, a dimensionless transient heat-conduction equation in polar coordinates is established and expresses K_uτ as a function of the Biot number Bi and the Fourier number Fo. The finite-volume method is employed for discretisation; the nodal radii and time steps are arranged in geometric progressions to guarantee accuracy during the violent unsteady stage while maintaining computational efficiency at later times. An in-house solver developed in Visual Studio is used to obtain high-precision discrete solutions over the ranges of different Bi and 0.01 ≤ Fo ≤ 1000. Through a variable transformation, a highly linear relationship between (Bi–K_uτ)⁻¹ and Fo^−0.5 is discovered, on the basis of which a unified quadratic-polynomial regression formula is constructed. The numerical results agree well with classical analytical solutions, validating the model and the code. The regression formula is concise and free of piecewise definitions; its average relative error is 1.8% and its maximum relative error is 4.2%, outperforming existing piecewise regressions. A case study shows that the unsteady heat-transfer dimensionless number drops to 29.0%, 7.7% and 5.0% of its initial value after 5 days, 1 year and 10 years of ventilation, respectively, consistent with field observations. A unified explicit expression of K_uτ valid over the entire continuous ranges of Bi and Fo is presented, eliminating the limitations of piece-wise fitting. Owing to its compact form, the formula can be directly embedded in mine air-temperature prediction software to achieve second-level accurate calculation of heat dissipation from surrounding rock for hundreds of roadways, offering a reliable and efficient tool for rapid thermal-hazard assessment and cooling design in deep mines. The method is readily extendable to non-circular cross-sections and heterogeneous rock, and future work will couple air temperature–humidity processes to enable dynamic prediction of the thermal environment of entire mines.