Abstract: Temperature difference leads to thermal deformation of the plane mirror, therefore affecting its working efficiency. In this paper, the fast boundary element method (BEM) based on quadratic element is applied for large-scale thermal analysis of the plane mirror. An introduction of the discontinuous element can treat the corner problem efficiently, and the new version of the fast multipole method is adopted to accelerate the BEM solution. A unified multipole expansion form for quadratic element is established to deal with mixed boundary conditions. In the numerical examples, both accuracy and efficiency of the fast multipole BEM are investigated and compared with the conventional algorithm. The proposed method is used to large-scale temperature calculation of the plane mirror and compared with finite element results. It is shown that the fast multipole BEM based on quadratic element is capable of large-scale 3-D thermal analysis with high accuracy.