A composite member includes a substrate composed of a composite material containing a metal and a non-metal. One surface of the substrate has spherical warpage of which radius of curvature R is not smaller than 5000 mm and not greater than 35000 mm. A sphericity error is not greater than 10.0 μm, the sphericity error being defined as an average distance between a plurality of measurement points on a contour of a warped portion of the substrate and approximate arcs defined by the plurality of measurement points. The substrate has a thermal conductivity not lower than 150 W/m·K and a coefficient of linear expansion not greater than 10 ppm/K.