One of the greatest challenges of humanity is to reach world climate-neutrality by 2050. Using renewable energy and in particular solar energy instead of fossil fuels, falls in this direction. A quest for the use of the solar energy as much as possible throughout the year becomes very important in this paradigm. A solution for the use of solar energy during the shading of the solar installation caused by clouds, for example, or even at night, is the use of the phase change materials (PCM). Also, to use the solar equipment as much as possible, the use of cascaded PCM appear as necessity. A transpired solar air collector equipped with cascaded PCM was numerically studied using a validated mathematical model, developed in MATLAB, for one specific autumn day in the temperate climate of Romania. Three different PCM with phase change temperatures of 24 °C (RT24), 26 °C (RT26) and 28 °C (RT28), were used for the PCM cascade. The air, the PCM spheres temperatures and the liquid mass fraction in three different zones of the thermal energy storage, at low, intermediate, and high temperature zones were studied. It is also noticeable the phase shift of each PCM zone, the first to release the heat is the RT28, then the RT26 and finally the RT24. The results showed that cascaded PCM storage could be used for an optimized heating/drying condition allowing to store an amount of energy during the first part of the day that could be released during drying time in the second part of the day. During daytime the LTHES stores thermal energy leading to a maximum decrease of air temperature of 4 °C. During night-time the LTHES released the thermal energy into the outlet air flow leading to a maximum increase of 8.4 °C. Analysing the liquid mass fraction of the PCMs, the results showed that only the RT24 zone is totally melting, with a maximum liquid mass fraction of 1, while the RT28 and RT26 reach a maximum liquid fraction at the centre of the sphere of 0.23 and 0.54, respectively.