We present a new approach for estimating the frequency of sub-hourly rainfall extremes in a warming climate with simulation by conditioning Bartlett–Lewis rectangular pulse (BLRP) rainfall model parameters on the mean monthly near surface air temperature. We use a censored modelling approach with multivariate regression to capture the sensitivity of the full set of BLRP parameter estimators to temperature enabling the parameter estimators to be updated. The downscaling framework incorporates uncertainty in climate model projections for moderate and severe carbon forcing scenarios by using an ensemble of climate model outputs. Linear regression on the logarithm of BLRP parameter estimators offers a robust model for parameter estimation with uncertainty. The approach is tested with 5 min rainfall data from Bochum in Germany, and Atherstone in the United Kingdom. We find that the approach is highly effective at estimating rainfall extremes in the present climate, and the estimation of future rainfall extremes appears highly plausible.