Multiphase flows are found in many energy processes, including water electrolysis and heat exchangers in nuclear engineering. In this context, bubble generation and dispersion are underlying physical mechanisms that need to be properly understood to ensure the optimal and safe operation of our devices. Simulations have become important tools to extract flow information at operating conditions otherwise difficult to capture with experiments. Despite high-fidelity multiphase numerical frameworks designed to model all relevant physics exist, e.g., [1], the multi-scale nature of such flows demands prohibitively fine grids to resolve all scales. For example, many fluids at conditions of interest have thermal and mass diffusivities that are one or two orders of magnitude lower than momentum diffusivity. Thus, resolving heat or mass transfer between the bubbles and the carrier fluid usually becomes a sub-grid resolution problem. This work focuses on the modelling of the thermal boundary layer (TBL) around deformable bubbles to predict the correct evaporation rates and bubble growth in the context of a multiphase flow simulation. Recently, it has been emphasized that semi-analytical models based on planar flows are not suitable when considering typical grid resolutions, i.e., the local curvature in the cell, and spherical models based on an osculating sphere have been proposed [2]. However, deformable bubbles are not represented by a single radius of curvature. Instead, a local paraboloidal representation of the interface for volume-of-fluid methods [3] is exploited to include the effects of two principal curvatures in the TBL model. Two different curvilinear coordinate systems are explored given the increased modelling complexity within boundary layer theory: (a) paraboloidal coordinates and (b) fitted curvilinear coordinates with a normal direction and two tangential directions. Neither coordinate system is free of approximations when targeting a TBL model, which results in additional errors that compete with the improved geometrical accuracy.