Mesoporous SBA-15 silica material was prepared by the sol–gel method and functionalized with thermosensitive polyethylenimine polymers with different molecular weight (g·mol−1): 800 (SBA-15(C)-800), 1300 (SBA-15(C)-1300) and 2000 (SBA-15(C)-2000). The nonsteroidal anti-inflammatory drug (NSAID) diclofenac sodium was selected as a model drug and encapsulated into the pores of prepared supports. Materials were characterized by the combination of infrared spectroscopy (IR), atomic force microscopy (AFM), transmission electron microscopy (TEM), photon cross-correlation spectroscopy (PCCS), nitrogen adsorption/desorption analysis, thermogravimetry (TG), differential scanning calorimetry (DSC) and small-angle X-ray diffraction (SA-XRD) experiments. The drug release from prepared matrixes was realized in two model media differing in pH, namely small intestine environment/simulated body fluid (pH = 7.4) and simulated gastric fluid (pH = 2), and at different temperatures, namely normal body temperature (T = 37 °C) and inflammatory temperature (T = 42 °C). The process of drug loading into the pores of prepared materials from the diclofenac sodium salt solutions with different concentrations and subsequent quantitative determination of released drugs was analyzed by UV-VIS spectroscopy. Analysis of prepared SBA-15 materials modified with polyethylenimines in solution showed a high ability to store large amounts of the drug, up to 230 wt.%. Experimental results showed their high drug release into the solution at pH = 7.4 for both temperatures, which is related to the high solubility of diclofenac sodium in a slightly alkaline environment. At pH = 2, a difference in drug release rate was observed between both temperatures. Indeed, at a higher temperature, the release rates and the amount of released drug were 2–3 times higher than those observed at a lower temperature. Different kinetic models were used to fit the obtained drug release data to determine the drug release rate and its release mechanism. Moreover, the drug release properties of prepared compounds were compared to a commercially available medicament under the same experimental conditions.