Heat engines, which cyclically transform heat into work, are ubiquitous in technology. Lasers and masers, which generate a coherent electromagnetic field, may be viewed as heat engines that rely on population inversion or coherence in the active medium. Here we put forward an unconventional paradigm of a remarkably simple electromagnetic heat-powered engine that bears basic differences to any known maser or laser: it does not rely on population inversion or coherence in its two-level working medium. Nor does it require any coherent driving or pump aside from two (hot and cold) baths. Strikingly, the proposed maser, in which the heat exchange between these baths mediated by the working medium amplifies the signal field, can attain the highest possible efficiency even if the signal is incoherent.