Automated machine learning (AutoML) strives for the automatic configuration of machine learning algorithms and their composition into an overall (software) solution -a machine learning pipeline -tailored to the learning task (dataset) at hand. Over the last decade, AutoML has become a hot research topic with hundreds of contributions. While AutoML offers many prospects, it is also known to be quite resource-intensive, which is one of its major points of criticism. The primary cause for a high resource consumption is that many approaches rely on the (costly) evaluation of many ML pipelines while searching for good candidates. This problem is amplified in the context of research on AutoML methods, due to large scale experiments conducted with many datasets and approaches, each of them being run with several repetitions to rule out random effects. In the spirit of recent work on Green AI, this paper is written in an attempt to raise the awareness of AutoML researchers for the problem and to elaborate on possible remedies. To this end, we identify four categories of actions the community may take towards more sustainable research on AutoML, namely approach design, benchmarking, research incentives, and transparency.