Heterogeneous membranes, otherwise known as Mixed Matrix Membranes (MMMs), which are used in gas separation processes, are the subject of growing interest. This is due to their potential to improve the process properties of membranes compared to those of homogeneous membranes, i.e., those made of polymer only. Using such membranes in a process involves subjecting them to varying temperatures and pressures. This paper investigates the effects of temperature and feed pressure on the process properties of homogeneous and heterogeneous membranes. Membranes made of Pebax®2533 copolymer and containing additional fillers such as SiO2, ZIF−8, and POSS-Ph were investigated. Tests were performed over a temperature range of 25–55°C and a pressure range of 2–8 bar for N2, CH4, and CO2 gases. It was found that temperature positively influences the increase in permeability, while pressure influences permeability depending on the gas used, which is related to the effect of pressure on the solubility of the gas in the membrane.