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With global temperatures approaching Paris climate agreement targets and a wide spread in modelled future warming, it is critical to rapidly identify any changes in warming rate. Here I address the question of when we would be able to detect acceleration of warming in global-mean temperature. Some standard techniques report significantly (p<0.05) accelerated warming over 1980—2020 in the latest versions of the three main datasets used in the IPCC Fifth Assessment Report, with a mean acceleration of 49 m°C/decade², which would add about 0.5°C additional warming over 50 years compared with linear warming. Accounting for El Nino, volcanism and solar activity using a published method, the acceleration is 36±30m°C/decade². Using large ensemble output, I show that statistical uncertainties are underestimated by several common approaches. I recommend a better-performing method and show that with these techniques 49m°C/decade² acceleration would likely not be detectable with robust confidence until at least 2026.