The study presents a novel physical-based statistical method, TENAX, for estimating extreme sub-hourly precipitation return levels. The model incorporates temperature as a covariate in a physically consistent manner and is based on a non-stationary and non-asymptotic theoretical framework. It combines a non-stationary statistical model for precipitation event magnitudes and an analytical probability density function for temperatures during precipitation events. The model is validated using data from a Swiss station and demonstrates its ability to reproduce sub-hourly precipitation return levels and observed properties of extreme precipitation. The TENAX model can project changes in extreme sub-hourly precipitation in a future warmer climate based on climate model projections of temperatures during wet days and changes in precipitation free-frequency. The model accounts for the physical relationship between temperature and extreme precipitation, which is crucial for climate change adaptation and resilience. The study highlights the importance of considering temperature-induced changes in atmospheric dynamics and the limitations of traditional extreme value distributions in capturing the physics of climate change. The TENAX model provides a flexible and physically consistent approach to estimating extreme precipitation return levels, which can be applied globally where sub-hourly precipitation data and near-surface air temperature are available. The model's ability to project changes in extreme precipitation is demonstrated using a case study in Switzerland, showing that temperature increases lead to higher precipitation return levels. The study also discusses the uncertainties associated with the model, its limitations, and its advantages in capturing the complex interactions between local and large-scale atmospheric processes. The TENAX model offers a promising tool for assessing the impacts of climate change on extreme precipitation events.The study presents a novel physical-based statistical method, TENAX, for estimating extreme sub-hourly precipitation return levels. The model incorporates temperature as a covariate in a physically consistent manner and is based on a non-stationary and non-asymptotic theoretical framework. It combines a non-stationary statistical model for precipitation event magnitudes and an analytical probability density function for temperatures during precipitation events. The model is validated using data from a Swiss station and demonstrates its ability to reproduce sub-hourly precipitation return levels and observed properties of extreme precipitation. The TENAX model can project changes in extreme sub-hourly precipitation in a future warmer climate based on climate model projections of temperatures during wet days and changes in precipitation free-frequency. The model accounts for the physical relationship between temperature and extreme precipitation, which is crucial for climate change adaptation and resilience. The study highlights the importance of considering temperature-induced changes in atmospheric dynamics and the limitations of traditional extreme value distributions in capturing the physics of climate change. The TENAX model provides a flexible and physically consistent approach to estimating extreme precipitation return levels, which can be applied globally where sub-hourly precipitation data and near-surface air temperature are available. The model's ability to project changes in extreme precipitation is demonstrated using a case study in Switzerland, showing that temperature increases lead to higher precipitation return levels. The study also discusses the uncertainties associated with the model, its limitations, and its advantages in capturing the complex interactions between local and large-scale atmospheric processes. The TENAX model offers a promising tool for assessing the impacts of climate change on extreme precipitation events.