The paper presents a novel physical-based statistical method, the TEmperature-dependent Non-Asymptotic statistical model for eXtreme return levels (TENAX), to estimate extreme sub-hourly precipitation return levels. This model incorporates temperature as a covariate in a physically consistent manner, addressing the limitations of current methods that often fail to capture the physics governing climate change. The TENAX model combines a non-stationary statistical model for precipitation event magnitudes with an analytical probability density function for temperatures during precipitation events. It is evaluated using data from several stations in Switzerland, demonstrating its ability to reproduce sub-hourly precipitation return levels and observed properties of extreme precipitation. The model is then used to 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 frequency. The results show that the TENAX model can effectively project sub-hourly precipitation extremes at different return levels, providing valuable insights for climate change adaptation and resilience. The paper also discusses the uncertainties, limitations, and advantages of the TENAX model, highlighting its potential for global application.The paper presents a novel physical-based statistical method, the TEmperature-dependent Non-Asymptotic statistical model for eXtreme return levels (TENAX), to estimate extreme sub-hourly precipitation return levels. This model incorporates temperature as a covariate in a physically consistent manner, addressing the limitations of current methods that often fail to capture the physics governing climate change. The TENAX model combines a non-stationary statistical model for precipitation event magnitudes with an analytical probability density function for temperatures during precipitation events. It is evaluated using data from several stations in Switzerland, demonstrating its ability to reproduce sub-hourly precipitation return levels and observed properties of extreme precipitation. The model is then used to 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 frequency. The results show that the TENAX model can effectively project sub-hourly precipitation extremes at different return levels, providing valuable insights for climate change adaptation and resilience. The paper also discusses the uncertainties, limitations, and advantages of the TENAX model, highlighting its potential for global application.