We investigate the combined effects of thermal expansion and gravity on the initiation and evolution of triple flames. In particular, we provide a possible criterion for the thermal energy per unit depth required for triple flame ignition by a cylindrical ignition kernel. Further, we describe the transient evolution of triple flames after initiation. Steady, non-propagating, planar solutions representing “flame tubes” are determined. The flame tube solutions are unstable; in time-dependent simulations it is found that initial perturbations increasing the thermal energy of flame tubes lead to the propagation of a triple flame, while perturbations decreasing the thermal energy lead to extinction. Therefore it is concluded that the thermal energy of flame tubes may be used to define a possible ignition energy per unit depth for planar triple flames in the mixing layer, analogous to spherical flame balls for spherically expanding flames. This is the first paper to provide a detailed study of the ignition energy of planar triple flames. When gravity is not taken into account, flame tubes subject to thermal expansion are found not to induce a flow, so that the flame tube energy can be determined without having to solve the full Navier–Stokes equations.