The generation of genuine multipartite entangled states is challenging in practice. Here we explore an alternative route to this task, via autonomous entanglement engines which use only incoherent coupling to thermal baths and time-independent interactions. We present a general machine architecture, which allows for the generation of a broad range of multipartite entangled states in a heralded manner. Specifically, given a target multiple-qubit state, we give a sufficient condition ensuring that it can be generated by our machine. We discuss the cases of Greenberger-Horne-Zeilinger, Dicke, and cluster states in detail. These results demonstrate the potential of purely thermal resources for creating multipartite entangled states useful for quantum information processing.