A simple and explicit burn criterion is presented, indicating whether a given temperature profile in a fusion plasma established by, for example, auxiliary heating, will evolve toward ignition or quench under the competing influence of alpha-particle heating and thermal conduction losses. The predictions are found to compare well with numerical simulations. The result is also used to demonstrate that peaked density and/or temperature profiles are advantageous from the point of view that the total plasma energy to be established by auxiliary heating in order to reach ignition is minimized.