Climate models are biased with respect to real world observations and usually need to be calibrated prior to impact studies. The suite of statistical methods that enable such calibrations is called bias correction (BC). However, current BC methods struggle to adjust for temporal biases, because they disregard the dependence between consecutive time-points. As a result, climate statistics with long-range temporal properties, such as heatwave duration and frequency, cannot be corrected accurately, making it more difficult to produce reliable impact studies on such climate statistics. In this paper, we offer a novel BC methodology to correct for temporal biases. This is made possible by i) re-thinking BC as a probability model rather than an algorithmic procedure, and ii) adapting state-of-the-art machine-learning (ML) probabilistic attention models to fit the BC task. With a case study of heatwave duration statistics in Abuja, Nigeria, and Tokyo, Japan, we show striking results compared to current climate model outputs and alternative BC methods.