Among the possible progenitor scenarios considered for Type Ia supernovae, those that involve a carbon–oxygen white dwarf (CO WD) accreting stably towards the Chandrasekhar mass should undergo a phase of hydrostatic carbon burning under high densities and strong convection: the simmering or carbon–flash phase, which can extend for a few hundred years before explosion. During this phase the progenitor CO WD can burn a small fraction of its carbon hydrostatically, releasing energy and ashes that make the star convective and able to capture electrons from the degenerate plasma. In this work we present simplified pre–supernova evolution models of CO WDs growing towards the Chandrasekhar mass accreting matter stably and evolving through the simmering phase towards ignition in order to explore the effects of different initial masses and cooling times in the final chemical composition of the WD before explosion. Preliminary results show that, as expected, denser systems at the start of the simmering phase undergo stronger neutronization. The amount of neutronization is less than what is found in the one–zone models of Chamulak et al. (2008), about a third, and can vary by about a factor of two depending on the exact path to explosion.