Numerical simulations of mantle convection with a composite temperature-dependent, Newtonian and non-Newtonian creep law have revealed a transition in the dominant creep mechanism with the increasing vigour of convection. Newtonian creep is found to dominate in the low Rayleigh number regime. With sufficiently high effective Rayleigh number, the overall creep mechanism in the convective flow becomes non-Newtonian. The transitional Rayleigh number increases strongly with the activation energy. These results would suggest a scenario that in the early epochs of Earth the flow in the mantle would have been governed by non-Newtonian rheology and would have exhibited both strong spatial and temporal fluctuations. With time the flow mechanism would behave like a Newtonian fluid and would have a different time-dependent character. In time-dependent Newtonian-dominated flows there are still localized features with distinctly non-Newtonian character. Our analysis of the relative contributions to the lateral viscosity field supports the idea that the inference of the nature of lateral viscosity heterogeneities by seismic tomography may be strongly contaminated by the dominant non-Newtonian contributions to the total lateral viscosity field.