This paper is concerned with the stationary plane contact of an insulated rigid punch and a half-space which is elastically anisotropic but thermally conducting. The frictional heat generation inside the contact region due to the sliding of the punch over the half-space surface and the heat radiation outside the contact region are taken into account. With the help of Fourier integral transform, the problem is reduced to a system of two singular integral equations. The equations are solved numerically by using Gauss-Jacobi and trapezoidal-rule quadratures. The effects of anisotropy and thermal effects are shown graphically.