To study phase-transition kinetics on submillisecond time scales a set of thin-film silicon-nitride gauges for ultra-fast scanning nanocalorimetry was constructed and utilized for controlled ultra-fast cooling, as well as heating, up to 10(6) K/s. In this paper an analytical solution for the model describing the heat transfer in a membrane gauge at ultra-fast heating and cooling is presented. The dynamics of the temperature distribution in the membrane gauge is calculated and compared with experimental data. The origin of limitations imposed on the maximum attainable controlled cooling rate is investigated. (C) 2014 Elsevier B.V. All rights reserved.