We contribute to the debate surrounding central banks and climate change by investigating how extreme temperatures affect medium-term inflation, the primary objective of monetary policy. Using panel local projections for 48 advanced and emerging market economies (EMEs), we study the impact of country-specific temperature shocks on a range of prices: consumer prices, including the food and non-food components, producer prices and the GDP deflator. Hot summers increase food price inflation in the near term, especially in EMEs. But over the medium term, the impact across the various price indices tends to be either insignificant or negative. Such effect is largely non-linear, being more significant for larger shocks and at higher absolute temperatures. We also provide simulations from a two-country model to understand the rationale behind the results. Overall, our results suggest that temperature plays a non-negligible role in driving medium-term price developments. Climate change matters for price stability.