It is well established that temperature variability affects a range of outcomes relevant to human welfare, including health (Gasparrini et al., 2017) emotion and mood (Baylis et al., 2018), and productivity across a number of economic sectors (Carleton & Hsiang, 2016; Dell et al., 2014). However, a critical and still unresolved empirical question is whether temperature variation has a long-lasting effect on economic productivity and, therefore, whether damages compound over time in response to long-lived changes in temperature expected with climate change. Several studies have identified a relationship between temperature and GDP (Burke et al., 2015; Dell et al., 2012; Kalkuhl & Wenz, 2020), but empirical evidence as to the persistence of these effects is still weak. This paper presents a novel approach to isolate the persistent component of temperature effects on output using lower frequency temperature variation. Using three different datasets we find that longer temperature anomalies affect GDP growth as much or more than short-lived anomalies, implying persistent and therefore cumulative effects of climate change on economic output. The population-weighted global effect of -0.8 pp per degree is sufficient to reduce per-capita income in 2100 by 44% under RCP6, approximately an order of magnitude larger than damages currently represented in cost-benefit integrated assessment models (Diaz & Moore, 2017).