The objective of this work is to assess the thermal behavior of a wall built with earth-based adobes and reinforced with fibers from the pinnate leaves of date palm available in abundance in Drâa Tafilalet region in southeast Morocco. A one-dimensional numerical simulation was carried out to estimate the influence of the thickness of the wall studied, on the thermal power exchanged and the thermal inertia of the building. In addition, several walls designed with different adobes based on different fiber content and thermal properties were investigated. The results of the numerical simulation show a maximum reduction of 46% of the flux passing through the walls containing 6% of date palm waste fibers. The time lag and the decrement factor of the heat flux have been improved ensuring good energy efficiency. In addition, the thermal inertia study of these walls with thicknesses from 22 to 30 cm, shows an increase in heat storage time of 0.39 h/cm and an increase in thermal resistance of 53%. A comparative study was carried out between two walls built by earthen adobes mixed with two different types of fibers indicates that the adobes containing pinnate leaves fibers present a better thermal inertia compared to the adobes containing palm mesh fibers.