In order to improve the performance of a solar still to a simple greenhouse, several experimental works have carried out from which we can enumerate the active distiller which represents a simple-effect solar still coupled with a solar collector and where the brine to be distilled is preheated. In order to increase the amount of distilled water, we set up an active solar still with a storage balloon of sensitive heat. Our prototype consists of a solar still with a simple greenhouse effect, having a metal cover which is considered as a condenser. A heat exchanger "tube type" is set up inside the basin to heat the distilled and where a good insulation is provided at the posterior side of the solar still. The aim of this work is to enrich the already available data by a mathematical modeling of the proposed prototype, which is based on the thermal balances and by using appropriate heat and mass coefficients aided by some simplifying assumptions. The aim of the simulation is also the optimization certain parameters that affect the production of distilled water and, as a result, having a certain appreciation about how will thermal storage contribute to a better performance of a solar still with a simple effect.