A methodology is proposed to design and predict operation of a solar collector for the desalination unit using the SMCEC principle. The corresponding dynamic model developed from the thermal energy and mass balances is based in the double infinite temperature hypothesis for the fluid and the absorber. This model represents an extension of the one-temperature model presented in a previous paper [1]. Two numerical methods are used for solving the corresponding model, The first method uses the well-known finite difference method, while the second solves the equations by using the functional approximation method. Experimental validation is carried out on the solar collector and the whole desalination unit to determine which of the two methods is most suited for theses studies. The good results confirm that the new theoretical model resolved with the orthogonal collocation method represents better the real behavior of the system and can be used to investigate the effect of various parameters on the performance of the collector and the production of the desalination unit.