Catalytic distillation is a technology that combines a heterogeneous catalytic reaction and the separation of reactants and products via distillation in a single reactor/distillation system. This process combines catalysis, kinetics, and mass transfer to obtain more selective products. The heterogeneous catalyst provides the sites for catalytic reactions and the porous surface for liquid/vapor separation. The advantages of catalytic distillation are energy savings, low waste streams, catalyst longevity, higher conversion, and product selectivity; these properties are interesting for petrochemical and petroleum industries. For this study, 100 mL of atmospheric residue of petroleum (ATR) was distilled in the presence of 1.0 g of a micro/mesoporous catalyst composed of a HY-MCM-41, and the reactor used was an OptiDist automatic distillation device, operating according to ASTM D-86 methodology. The products were collected and analyzed by gas chromatography. The samples of ATR, HY/ATR, and HY-MCM-41/ATR were analyzed by thermogravimetry (TG) to determine the activation energies (Ea) relative to the thermal decomposition of the process, using the Ozawa–Flynn–Wall (OFW) kinetic model. The obtained results show a potential catalytic distillation system for use in the reaction of heavy petroleum fractions and product separation from the HY/MCM-41 micro/mesoporous catalyst. The TG data revealed two mass loss events for ATR in the ranges of 100–390 and 390–590 °C, corresponding to volatilization and thermal cracking, respectively. The Ea determined for the thermal degradation of the ATR without a catalyst was in the range of 83–194 kJ/mol, whereas in the presence of the HY-MCM-41 catalyst, it decreased to 61–105 kJ/mol, evidencing the catalytic effect of the micro-mesoporous material. The chromatography analysis allowed for the identification of gasoline and a major production of diesel and gasoil when the HY-MCM-41 mixture was used as the catalyst, evidencing the synergism of the combined effect of the acid sites, the crystalline phase, and the microporosity of the HY zeolite with the accessibility of the hexagonal mesoporous structure of the MCM-41 material.