Climate change, through temperature anomalies, is likely to have an asymmetric effect on prices and economic activity within the euro area. In this paper, we aim to measure the monetary stress for each member country resulting from these asymmetric shocks. For that purpose, we first measure how inflation and GDP per capita respond to temperature anomalies in several euro area countries. As a second step, we simulate the temperature-induced changes in inflation and GDP per capita over the period 2025-2100. The significant divergences in these temperature-induced variables call for different monetary policy needs within the currency union, hence the existence of a temperature-induced monetary stress that is likely to worsen over time. Our results provide evidence that climate change constitutes a challenge to the sustainability of the currency union and to the one size fits all ECB's policy.