In this paper, we present a theoretical investigation as a function of temperature of a critical anomaly find in InAlAs hetero-structure of two-dimensional electron gas. This study has shown the presence of a large and continuous anomaly. This anomaly is explained through a theory based on the general assumption. The present theoretical research is based essentially on the characteristic of specific heat capacity extending over a large temperature, but we underline a good agreement with results of the relation with chemical potential and Broadening parameter as a function of temperature. It is found that the specific heat capacity observed by a peak at low temperature, at a critical temperature, is directly linked to Schottky anomaly and unveiling the existence of phase transition in InAlAs. Our results are completed by the study of the dependence of the heat capacity on the spin as a function of temperature. This study confirms the same behavior with result without spin.