In a changing climate, there is an ever-increasing societal demand for accurate and reliable interannual predictions. Accurate and reliable interannual predictions of global temperatures are key for determining the regional climate change impacts that scale with global temperature, such as precipitation extremes, severe droughts, or intense hurricane activity, for instance. However, the chaotic nature of the climate system limits prediction accuracy on such timescales. Here we develop a novel method to predict global-mean surface air temperature and sea surface temperature, based on transfer operators, which allows, by-design, probabilistic forecasts. The prediction accuracy is equivalent to operational forecasts and its reliability is high. The post-1998 global warming hiatus is well predicted. For 2018–2022, the probabilistic forecast indicates a warmer than normal period, with respect to the forced trend. This will temporarily reinforce the long-term global warming trend. The coming warm period is associated with an increased likelihood of intense to extreme temperatures. The important numerical efficiency of the method (a few hundredths of a second on a laptop) opens the possibility for real-time probabilistic predictions carried out on personal mobile devices.