AbstractWe consider issues related to the effect of climate change on the persistence of (trend‐corrected) temperatures using global gridded data for both land and oceans. We first discuss how the presence of trends and additive noise affects inference about persistence. Ignoring a trend induces an upward bias, while not accounting for noise induces a downward bias. We show that the increase in persistence in the commonly used Warm Spell Duration Index is simply an artifact of increasing temperatures. To purge the impact of both trends and noise, we adopt a simple state‐space model. Of separate interest, we document a much larger noise component for land than for oceans. The estimates of the persistence are much larger for oceans than for land. Inspection of the estimates across various subsamples and the application of tests for structural changes suggest the same pattern of persistence for both land and oceans across time, with few minor exceptions. Hence, our results show that surface temperature persistence has remained constant during the observed period.