In their comment on our paper (Caesar et al 2020 Environ. Res. Lett. 15 024003), Chen and Tung (hereafter C&T) argue that our analysis, showing that over the last decades Atlantic meridional overturning circulation (AMOC) strength and global mean surface temperature (GMST) were positively correlated, is incorrect. Their claim is mainly based on two arguments, neither of which is justified: first, C&T claim that our analysis is based on ‘established evidence’ that was only true for preindustrial conditions—this is not the case. Using data from the modern period (1947–2012), we show that the established understanding (i.e. deep-water formation in the North Atlantic cools the deep ocean and warms the surface) is correct, but our analysis is not based on this fact. Secondly, C&T claim that our results are based on a statistical analysis of only one cycle of data which was furthermore incorrectly detrended. This, too, is not true. Our conclusion that a weaker AMOC delays the current surface warming rather than enhances it, is based on several independent lines of evidence. The data we show to support this covers more than one cycle and the detrending (which was performed to avoid spurious correlations due to a common trend) does not affect our conclusion: the correlation between AMOC strength and GMST is positive. We do not claim that this is strong evidence that the two time series are in phase, but rather that this means that the two time series are not anti-correlated.