There is growing notion that black holes may not contain curvature singularities (and that indeed nature in general may abhor such spacetime defects). This notion could have implications on our understanding of the evolution of primordial black holes (PBHs) and possibly on their contribution to cosmic energy. This paper discusses the evolution of a non-singular black hole (NSBH) based on a recent model [1]. We begin with a study of the thermodynamic process of the black hole in this model, and demonstrate the existence of a maximum horizon temperature T_{max}, corresponding to a unique mass value. At this mass value the specific heat capacity C changes signs to positive and the body begins to lose its black hole characteristics. With no loss of generality, the model is used to discuss the time evolution of a primordial black hole (PBH), through the early radiation era of the universe to present, under the assumption that PBHs are non-singular. In particular, we track the evolution of two benchmark PBHs, namely the one radiating up to the end of the cosmic radiation domination era, and the one stopping to radiate currently, and in each case determine some useful features including the initial mass m_{f} and the corresponding time of formation t_{f}. It is found that along the evolutionary history of the universe the distribution of PBH remnant masses (PBH-RM) PBH-RMs follows a power law. We believe such a result can be a useful step in a study to establish current abundance of PBH-MRs.
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