ABSTRACTThe IPCC predicts that events at the extreme tail of the probability distribution will increase at a higher rate relative to less severe but still abnormal events. Such outlier events are of particular concern due to nonlinear physiological and demographic responses to climatic exposure, meaning that these events are expected to have disproportionate impacts on populations over the next decades (so called low‐likelihood, high‐impact events —LLHI). Because such events are historically rare, forecasting how biodiversity will respond requires mechanistic models that integrate the fundamental processes driving biological responses to our changing climate. Here we built a matrix population model (MPM) from long‐term monitored populations of an insect model species in a Mediterranean area. The model simultaneously integrates the effects of extreme microclimatic heat exposure and drought‐induced host‐plant scarcity on early life stages, a key methodological step forward because these understudied life stages are usually very susceptible to climatic events. This model for the first time allowed us to forecast the demographic impacts that LLHI events will have on a well‐known insect considering their whole life cycle. We found that juveniles were the life stage with the largest relative contribution to population dynamics. In line with field observations, simulated population rates in current climatic regimes were importantly determined by drought impacts, producing a regional mosaic of non‐declining and declining populations. The simulations also indicated that in future, climate scenarios not meeting the Paris Agreement, LLHI heat extremes triggered regionally widespread and severe declines in this currently abundant species. Our results suggest that LLHI events could thus emerge as a critical new —but overlooked— driver of the declines in insect populations, risking the crucial ecosystem functions they perform. We suggest that process‐based and whole‐cycle modelling approaches are a fundamental tool with which to understand the true impacts of climate change.