Ultrafast nanocalorimetry on the basis of thin-film gauges was developed and utilized for studying phase-transition kinetics in thin-film samples. Ultrafast measurements at increasing rates of temperature change require a comprehensive analysis of the heat conduction processes. In this paper the analysis of the fast thermal response in thin-film samples at the boundary conditions corresponding to ultrafast calorimetric gauges is performed. The effects of interfacial thermal contact resistance and non-Fourier heat conduction are calculated analytically. The limits of validity of the classical diffusive heat conduction theory at high-frequency temperature-modulation measurements are studied. The alternatives of Fourier and non-Fourier heat conduction are considered. The conditions optimal for detection of the effect of non-Fourier heat conduction are defined. (C) 2016 Elsevier B.V. All rights reserved.