In the context of rapid human-caused climate change, regular updates of the state of knowledge of current and future climate are needed. New statistical methods using observational constraints underpinned estimates of present-day human-induced warming and projected future warming in the most recent IPCC report. As time goes by, and new updated observational records become available, how should estimates of the current and projected human-caused climate change be updated? Here, we use a perfect model framework and show that incorporating observations from every new year in observationally constrained projections improves their accuracy, without causing major year-to-year spurious variability on outcomes. The forced warming estimated for the current year also exhibits high enough stability to be considered as a robust indicator of the state of the climate system.