A 27-residue lattice heteropolymer subject to Monte, Carlo dynamics on a simple cubic lattice is studied over a range of temperatures. Folding time distributions are used to obtain information concerning the details of folding kinetics. The results are compared with those from methods based on mean force surfaces expressed in terms of a reduced set of variables and on a disconnectivity graph for the same system. A detailed analysis of the folding trajectories is given, and the importance of dead-end traps in determining the folding time is demonstrated. We show that the calculated folding kinetics can be modeled by a system of kinetic equations, with the essential rate constants determined from the Monte Carlo simulations and the resulting folding time distributions. The kinetic equations make possible an analysis of the variation of the importance of different channels with temperature. In particular, we show that the presence of intermediates may be masked in the folding time distributions, with the mean folding time being independent of the height of the barrier between the intermediates and collapsed globule state of the system. This and other results demonstrate that care has to be used in interpreting experimental folding data in terms of the underlying kinetics. Correspondingly, simulations are shown to have to satisfy certain requirements to obtain proper sampling of the dead-end traps.