Climate impacts on economic productivity indicate that climate change may threaten price stability. Here we apply fixed-effects regressions to over 27,000 observations of monthly consumer price indices worldwide to quantify the impacts of climate conditions on inflation. Higher temperatures increase food and headline inflation persistently over 12 months in both higher- and lower-income countries. Effects vary across seasons and regions depending on climatic norms, with further impacts from daily temperature variability and extreme precipitation. Evaluating these results under temperature increases projected for 2035 implies upwards pressures on food and headline inflation of 0.92-3.23 and 0.32-1.18 percentagepoints per-year respectively on average globally (uncertainty range across emission scenarios, climate models and empirical specifications). Pressures are largest at low latitudes and show strong seasonality at high latitudes, peaking in summer. Finally, the 2022 extreme summer heat increased food inflation in Europe by 0.43-0.93 percentage-points which warming projected for 2035 would amplify by 30-50%.