In this work, the design and characterization of new supported ionic liquid membranes, as medium-temperature polymer electrolyte membranes for fuel-cell application, are described. These membranes were elaborated by the impregnation of porous polyimide Matrimid® with different synthesized protic ionic liquids containing polymerizable vinyl, allyl, or methacrylate groups. The ionic liquid polymerization was optimized in terms of the nature of the used (photo)initiator, its quantity, and reaction duration. The mechanical and thermal properties, as well as the proton conductivities of the supported ionic liquid membranes were analyzed in dynamic and static modes, as a function of the chemical structure of the protic ionic liquid. The obtained membranes were found to be flexible with Young’s modulus and elongation at break values were equal to 1371 MPa and 271%, respectively. Besides, these membranes exhibited high thermal stability with initial decomposition temperatures > 300 °C. In addition, the resulting supported membranes possessed good proton conductivity over a wide temperature range (from 30 to 150 °C). For example, the three-component Matrimid®/vinylimidazolium/polyvinylimidazolium trifluoromethane sulfonate membrane showed the highest proton conductivity—~5 × 10−2 mS/cm and ~0.1 mS/cm at 100 °C and 150 °C, respectively. This result makes the obtained membranes attractive for medium-temperature fuel-cell application.