We studied within the framework of a mean-field approach the nonequilibrium dyn amic phase transition of a kinetic Ising spin system subject to a perturbative f ield and temperature simultaneously by comparison between time-dependent Ginzbur g-Landau and Glauber dynamics models. The dynamic phase transition (DPT) boundar ies, separating a symmetry-breaking dynamic ordered phase from its symmetric dyn amic disordered counterpart, were identified through a systematic simulation of the above two models. The dependence of the dynamic order parameter Q and the fo urth order cumulant ratio U upon the temperature t(r0), the frequency ω and amplitude h0 of driving field were also investigated in detai l. A discussion was presented concerning the current controversies on whether bo th a discontinuous dynamic phase transition occurs possibly below a specific low temperature and a tri-critical point exists on the DPT boundary in a kinetic Is ing spin system.