This paper reports a semi-analytical model for studying general and critical heat-transfer characteristics at the interface between a coated sheet and a moving coated tool tip in incremental forming considering heat partition. Both of the tool tip and the sheet can be treated as a coating-substrate material system. The frequency response functions (FRFs) for temperature rise in each material system are analytically derived, in which the tool-tip velocity is incorporated by means of the Galilean transform. The FRFs are then converted into influence coefficients (ICs) in the frequency domain for solution efficiency and convenience. Fast numerical techniques are applied, such as the conjugate gradient method (CGM) for searching the distributed tool-tip/sheet heat partition and the fast Fourier transform (FFT) for obtaining temperature solutions. The proposed model is implemented to analyze the combined influences of Peclet number, coating thicknesses of the tool tip and the sheet, sheet thickness, and heat conductivity of each material on the temperature rise and the heat partition at the interface, and the sensitivity of the dependence of the peak temperature on these system parameters. (C) 2018 Elsevier Ltd. All rights reserved.