In this paper, the boundary integral equation and the fundamental solution of axisymmetric transient heat conducation problem are derived from the boundary integral equation and fundamental solution of three dimension transient potential problem, and given in discretization form of the boundary element equation. On this basis, several axisymmetric thermal problems with different boundary conditions are calculated. Obtained results show that the method formed in this pape is reliable, and have good accuracy and good stability. It can be used to analyze the temperature field of axisymmetric body in engineering.