Extreme event attribution is about estimating probabilities of extreme weather events and characterizing how they have changed, or will change in the future, as a consequence of greenhouse-gas-induced climate change. The approach proposed here is conditional in the sense that the extreme event probabilities are conditioned on some regional weather variable, such as summer mean annual temperature averaged over a grid box, that  we may reasonably hope to be well represented by climate models. The estimation problem is in three steps, (a) modeling the conditional distribution of extremes given the regional variable, (b) modeling the conditional distribution of the regional variable given climate model output, (c) combining steps (a) and (b) to model the conditional distribution of extremes given climate model output at various time points in the past and, using forward simulations of climate models, the future. The analysis relies entirely on public data sources including daily station data from the Global Historical Climatological Network, gridded temperature monthly averages from the Climate Research Unit of the University of East Anglia, and climate model from the CMIP6 archive. As an example, I estimate the probability of a temperature over 40 degrees C at London's Heathrow Airport (an event that occurred on July 19 this year) based on data available prior to 2022. The estimated probability is about 7 times larger for 2022 than for the mid-20th century, but is projected to grow rapidly in the future, especially under the pessimistic ssp585 emissions scenario.