Heat load on beamline optics is a serious obstacle for devices designed to generate pure linearly polarized photons in third generation synchrotron radiation facilities. For permanent magnet undulators, this problem can be overcome by implementing a figure-eight design configuration. As yet there has been no good method to tackle this problem for electromagnetic elliptical undulators. Here, a novel design and operational mode is suggested, which can generate pure linearly polarized photons with very low on-axis heat load. Additionally, the minimum photon energy capability of linearly polarized photons can be significantly extended by this method.