Steady and transient heat convection in axisymmetric stagnation point flow with momentum and thermal slip effects are studied numerically for different flow parameters. The thermal response to time-dependent wall temperature variations in surface cooling and heating processes is analyzed in terms of temporal variations in the heat transfer coefficient, thermal jump, and fluid temperature at the surface. The transition time from an initial to a final steady state is also investigated over a range of slip factor and decay/growth rate of the wall temperature. A criterion in the form of a relation between Prandtl number and the specific heat ratio that characterizes the variation of the convective heat transfer coefficient with the slip factor is established. The results presented show that the convective heat transfer coefficient is less influenced by transient conditions as rarefaction increases. Higher Prandtl number flows are more influenced by transients. The transition time is found to increase with slip and decrease with the decay/growth rate of the wall temperature and is most influenced at relatively low values of both slip and decay/growth rate of the wall temperature.