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The challenge that climate change poses to humanity has spurred a rapidly developing field of artificial intelligence research focused on climate change applications. The climate change AI (CCAI) community works on a diverse, challenging set of problems which often involve physics-constrained ML or heterogeneous spatiotemporal data. It would be desirable to use automated machine learning (AutoML) techniques to automatically find high-performing architectures and hyperparameters for a given dataset. In this work, we benchmark popular AutoML libraries on three high-leverage CCAI applications: climate modeling, wind power forecasting, and catalyst discovery. We find that out-of-the-box AutoML libraries currently fail to meaningfully surpass the performance of human-designed CCAI models. However, we also identify a few key weaknesses, which stem from the fact that most AutoML techniques are tailored to computer vision and NLP applications. For example, while dozens of search spaces have been designed for image and language data, none have been designed for spatiotemporal data. Addressing these key weaknesses can lead to the discovery of novel architectures that yield substantial performance gains across numerous CCAI applications. Therefore, we present a call to action to the AutoML community, since there are a number of concrete, promising directions for future work in the space of AutoML for CCAI. We release our code and a list of resources at https://github.com/climate-change-automl/climate-change-automl.