Frontal photopolymerisation (FPP) is a rapid and versatile solidification process that can be used to fabricate complex three-dimensional structures by selectively exposing a photosensitive monomer-rich bath to light. A characteristic feature of FPP is the appearance of a sharp polymerisation front that propagates into the bath as a planar travelling wave. In this paper, we introduce a theoretical model to determine how heat generation during photopolymerisation influences the kinetics of wave propagation as well as the monomer-to-polymer conversion profile, both of which are relevant for FPP applications and experimentally measurable. When thermal diffusion is sufficiently fast relative to the rate of polymerisation, the system evolves as if it were isothermal. However, when thermal diffusion is slow, a thermal wavefront develops and propagates at the same rate as the polymerisation front. This leads to an accumulation of heat behind the polymerisation front which can result in a significant sharpening of the conversion profile and acceleration of the growth of the solid. Our results also suggest that a novel way to tailor the dynamics of FPP is by imposing a temperature gradient along the growth direction.