Following from the new formulations of Chap. 4 , here the focus is on Stefan problems where the phase change temperature is a variable. In the first section, physical reasons for this change are discussed and quantified. Models for the solidification of supercooled fluids, where the phase change temperature varies with the front velocity, are analysed for both linear and nonlinear kinetic undercooling cases. At the nanoscale, the phase change temperature may vary due to curvature-induced stress, and this effect is investigated for the melting of spherical nanoparticles and nanowires. The variable temperature effect can help explain the experimentally observed sudden disappearance of nanoparticles. An analogous problem in mass transfer, concerning the growth of nanocrystals from a monomer solution, is also presented. Here the solubility (equivalent to the phase change temperature) varies with crystal size. By introducing multiple crystals, the effect of Ostwald ripening, where smaller particles dissolve and are then consumed by larger particles, is explained.