Frontal polymerization is a process of converting a monomer into a polymer by means of a self-propagating, thermal reaction wave. We study initiation of polymerization waves by a heat source. A five-species reaction model is considered with a focus on the evolution of two of these species and the temperature of the mixture. We conduct independent numerical analyses of two experimental configurations. The first of these consists of a mixture of monomer and initiator (a catalytic agent) placed in a test tube and a constant high temperature imposed at one end of the tube. Here, we identify four parameters whose values are determined by the rate of initiator decomposition, amount of volumetric heat loss, amount of heat produced by chemical conversion, and initial mixture temperature. We present a marginal initiation criterion as a relation between these parameters. The second experimental configuration considered here involves placing a test tube filled with a monomer and initiator mixture into a hot thermostatic oil bath. Asakur et al. recently reported that they had observed the formation of a reaction front in the center of a mixture under these conditions. We offer a simple mathematical model of this experiment and the results of numerical simulations based on this model. We show that the model proposed here captures a phenomenon observed in experiment, namely, that for a given bath temperature, there is a minimal tube radius necessary for a reaction front to be initiated. Our results further confirm that the frontal polymerization observed in such experiments can occur via a thermal mechanism. (~) 2005 Elsevier Ltd. All rights reserved.