Modern tools for natural language generation may enable novel forms of scholarly fraud based on the automatic generation of fake review reports for academic papers, i.e., of a few sentences broadly related to the textual content of a submission and written with the style of an anonymous reviewer. A tool capable of generating such reports automatically and for free could enable various forms of unethical behavior by publishers and researchers. In this work we experiment with a simple heuristic that makes use of widely available and easy to use tools for natural language generation, including the Generative Pretrained Transformer 2 (GPT-2), in order to craft fake reviews automatically. We also perform a small user study for assessing the credibility of those reviews. Our analysis suggests that academic frauds based on fake reviews may indeed be feasible and ready to be deployed in the wild.