The importance of climate change for driving adverse climate impacts has motivated substantial effort to understand the rate and magnitude of regional climate change in different parts of the world. However, despite decades of research, there is substantial uncertainty in the time remaining until specific regional temperature thresholds are reached, with climate models often disagreeing both on the warming that has occurred to-date, as well as the warming that might be experienced in the next few decades. Here, we adapt a recent machine learning approach to train a convolutional neural network to predict the time (and its uncertainty) until different regional warming thresholds are reached based on the current state of the climate system. In addition to predicting regional rather than global warming thresholds, we include a transfer learning step in which the climate-model-trained network is fine-tuned with limited observations, which further improves predictions of the real world. Using observed 2023 temperature anomalies to define the current climate state, our method yields a central estimate of 2040 or earlier for reaching the 1.5 °C threshold for all regions where transfer learning is possible, and a central estimate of 2040 or earlier for reaching the 2.0 °C threshold for 31 out of 34 regions. For 3.0 °C, 26 °C out of 34 regions are predicted to reach the threshold by 2060. Our results highlight the power of transfer learning as a tool to combine a suite of climate model projections with observations to produce constrained predictions of future temperatures based on the current climate.