Extreme sub-hourly precipitation, typically convective in nature, is capable of triggering natural disasters such as floods and debris flows. A key component of climate change adaptation and resilience is quantifying the likelihood that sub-hourly extreme precipitation will exceed historical levels in future climate scenarios. Despite this, current approaches to estimating future sub-hourly extreme precipitation return levels are deemed insufficient. The reason for this can be attributed to two factors: there is limited availability of data from convection-permitting climate models (capable of simulating sub-hourly precipitation adequately) and the statistical methods we use to extrapolate extreme precipitation return levels do not capture the physics governing global warming. We present a novel physical-based statistical method for estimating the extreme sub-hourly precipitation return levels. The proposed model, named TEmperature-dependent Non-Asymptotic statistical model for eXtreme return levels (TENAX), is based on a parsimonious non-stationary and non-asymptotic theoretical framework that incorporates temperature as a covariate in a physically consistent manner. We first explain the theory and present the TENAX model. Using data from several stations in Switzerland as a case study, we demonstrate the model's ability to reproduce sub-hourly precipitation return levels and some observed properties of extreme precipitation. We then illustrate how the model can be utilized to project changes in extreme sub-hourly precipitation in a future warmer climate only based on climate model projections of temperatures during wet days and on foreseen changes in precipitation frequency. We conclude by discussing the uncertainties associated with the model, its limitations, and its advantages. With the TENAX model, one can project sub-hourly precipitation extremes at different return levels based on daily scale projections from climate models in any location globally where observations of sub-hourly precipitation data and near-surface air temperature are available.