As electronic devices decrease in size, heat management at the nanoscale becomes a crucial issue. Nanoscale heat flow may be significantly different to that at the macroscale: At the macroscale, due to the large number of phonons and consequent frequent collisions, the process may be viewed as diffusive; at the nanoscale, thermal energy transport may be viewed as a ballistic process driven by infrequent, random collisions. The breakdown of Fourier’s law, at both small length and time scales, has been predicted theoretically, demonstrated via molecular dynamics and observed experimentally. In this chapter, we begin by analysing heat flow in a nanowire through the Guyer-Krumhansl (GK) formulation, rather than Fourier’s law. Once the GK equation has been established as a reliable descriptor of heat flow at the nanoscale, we extend the equations to deal with a one-dimensional phase change problem. Results from GK, Maxwell-Cattaneo, and Fourier models are compared for a solidifying silicon material, demonstrating a similarity in the phase change rate but significant differences in the heat flow behaviour.