We have proposed a model to analyze the growth kinetics of lysozyme crystals/aggregates under non-isothermal conditions. The model was formulated through an analysis of the entropy production of the growth process which was obtained by taking into account the explicit dependence of the free energy on the temperature. We found that the growth process is coupled with temperature variations, resulting in a novel Soret-type effect. We identified the surface entropy of the crystal/aggregate as a decisive ingredient controlling the behavior of the average growth rate as a function of temperature. The behavior of the Gibbs free energy as a function of temperature is also analyzed. The agreement between theory and experiments is very good in the range of temperatures considered.