The paper describes a coupling of the geometric Volume-of-Fluid (VOF) method with a sharp-interface phase-change model for Cartesian and axisymmetric grids. Both the interfacial position and the temperature field are resolved with subgrid accuracy. Species transport with implicit diffusion is considered in the gas phase. The numerical implementation of the method developed here is described in detail, as well as its coupling with the incompressible Navier-Stokes solver PSI-BOIL, which features a hybrid, finite-volume/finite-difference approach based on a fixed, rectangular grid. Several verification cases have been undertaken to ensure correct implementation of the method in the code and to evaluate its performance. These include simulations of the Stefan problem, sucking problem and bubble growth in superheated liquid. In all cases, very good agreement with the analytical solution has been reached and grid convergence has been demonstrated. Simulations of evaporating and condensing rising bubbles, for which high-quality measured data are available, are also presented to serve as validation tests. Reasonable agreement of simulation results with experimental data has been recorded and applicability of the method to problems without inherent symmetry and featuring turbulence is shown. This work represents the first successful application of a geometric VOF method coupled with a sharp-interface phase-change model and species transport to non-trivial problems. The achieved performance of our algorithm in the verification and validation exercise represents an important step in the development of multiphase codes capable of accurately resolving complex three-dimensional multiphase flows. (C) 2021 The Author(s). Published by Elsevier Ltd.