The outer edge radius temperature tends to zero when control-heat circle of roadway surrounding rock to be stable,can be interpreted as:“when the control-heat circle tends to be stable,at radius R0,the circle surface of the surrounding rock, the conduction of per unit area heat tends to zero”,and this characteristic was described as the second boundary-condition for the solutions of heat conduction differential equation in the control-heat circle,in this way,avoided the complicated integral problems of temperature distribution and reduced the difficulty;by the method of variables separation,the heat conduction differential equation in rocks converted to Sturm-Liouville problems;through introducing the eigenfunction and norm,and using the Fourier-Bessel series expansion and the integral properties of Bessel function,the wall surface temperature gradient and the unsteady heat transfer coefficient formula in roadway surrounding rock was obtained.By using the computing functions of MATLAB software,the reliability and accuracy of the unsteady heat transfer coefficient formula were compared and analyzed in roadway surrounding rock,the results showed that the temperature distribution function in rocks and the unsteady heat transfer coefficient formula are correct and believable.