In June 2021, Canada experienced an intense heat wave with unprecedented temperatures and far-reaching socio-economic consequences. Anomalous rainfall in the West Pacific triggers a cascade of weather events across the North Pacific, which build up a high-amplitude ridge over Canada and ultimately lead to the heat wave. We show that the response of the jet stream to diabatically enhanced ascending motion in extratropical cyclones represents a predictability barrier with regard to the heat wave magnitude. Therefore, probabilistic weather forecasts are only able to predict the extremity of the heat wave once the complex cascade of weather events is captured. Our results highlight the key role of the sequence of individual weather events in limiting the predictability of this extreme event. We therefore conclude that it is not sufficient to consider such rare events in isolation but it is essential to account for the whole cascade over different spatio-temporal scales.