Understanding and estimating regional climate change under different anthropogenic emission scenarios is pivotal for informing societal adaptation and mitigation measures. However, the high computational complexity of state-of-the-art climate models remains a central bottleneck in this endeavour. Here we introduce a machine learning approach, which utilises a unique dataset of existing climate model simulations to learn relationships between short-te¬rm and long-term temperature responses to different climate forcing scenarios. This approach not only has the potential to accelerate climate change projections by reducing the costs of scenario computations, but also helps uncover early indicators of modelled long-term climate responses, which is of relevance to climate change detection, predictability and attribution. Our results highlight challenges and opportunities for data-driven climate modelling, especially concerning the incorporation of even larger model datasets in the future. We therefore encourage extensive data sharing among research institutes to build ever more powerful climate response emulators, and thus to enable faster climate change projections.