Within the framework of a one dimensional study, the accuracy is examined of two kinds of flux limited diffusion model: one is the artificially flux limited model developed by Corman and the other is based on the Levermore-Pomraning theory, for evaluating the alpha particle heating rate in laser imploded DT targets. It is found that the former model cannot correctly evaluate the ignition condition and the gain since it significantly underestimates the heating rate in the region where alpha particles are born. Contrary to this: in the latter model, which can estimate well the profile of the alpha particle heating rate, not only the time integrated burn properties but also the fuel evolution in space and time are in good agreement with results obtained on the basis of accurate transport calculations.