Extreme-weather events frequently drive production fluctuations, price volatility, and hence uncertainty on agricultural commodity markets. Simulation models of global agriculture typically assume normal weather in deterministic scenarios, contain no explicit parameterization of weather elements on the supply side, and confound multitudinous sources of yield fluctuation in exogenous yield shocks. As a part of a wider project on extreme events modelling, in this paper we present the experimental design of a first attempt to explicitly parameterize extreme weather into a partial equilibrium model of global agriculture (Aglink-Cosimo). We outline the main model additions and present preliminary estimates of wheat yield-to-heat elasticities for key regions. We also present the potential wheat market impacts from a counterfactual heat-wave scenario in Australia. Finally, we outline ongoing and future work on multi-scenario analysis in the context of extreme weather and global markets.