An analytical investigation is made of the time evolution of the 1-D temperature profile in a fusion reactor plasma where the nonlinear energy balance equation is dominated by alpha-particle heating and thermal conduction losses. Special emphasis is given to the problem of establishing sufficient conditions for the transition to thermonuclear burn for given initial temperature profiles. In particular, it is demonstrated that for strongly nonlinear alpha-particle heating, temperature profiles initially peaked on-axis are more easily ignited than profiles similar in form to the equilibrium profile of the energy balance equation. Simple analytical criteria for ignition are established and are shown to compare favourably with results of numerical calculations.