The ignition and burn dynamics of low temperature ignition (LTI) targets are investigated by means of one dimensional (1-D) coupled transport-hydrodynamics simulations, in which the stagnation dynamics is appropriately taken into account. In this scheme, ignition takes place in the central region of the fuel and then the burn wave propagates outward owing to heating of the fusion products, without the production of a strong shock wave. The ignition condition in the LTI scheme is presented in terms of the usual ρR - T criterion and of the required implosion velocity. A scaling law for the limiting energy gain is proposed. It is shown that with enough fuel confinement (high ρR), higher energy gains can be achieved than those obtained in the previous model with volume ignited, uniformly compressed targets. (The limiting gain is about 1.5 times larger than that in the `volume ignition' computations.) Without sufficient confinement, on the contrary, the bremsstrahlung loss during the stagnation phase increases rapidly, which significantly lowers the energy gain.