The selective thermal pervaporation (TPV) of dilute aqueous mixtures of 1-butanol through a hydrophobic poly(1-trimethylsilyl-1-propyne) (PTMSP) membrane in plate-and-frame modules with an air gap has been investigated experimentally and theoretically for the first time. The dependences of the composition and the permeate flow on the temperature and initial concentration of the mixture, the liquid coolant temperature, and the membrane thickness have been measured. It has been shown that a permeate flow across the PTMSP membrane can be achieved in the TPV mode that is not inferior to that of vacuum pervaporation at condensation temperatures of 0.5-15.0 degrees C. The permeation and diffusion activation energies have been estimated from the measured temperature dependences of the partial fluxes. Equations for the TPV process have been derived in terms of the one-dimensional resistance model. The temperature dependences of the diffusion coefficients of 1-butanol and water in the membrane have been determined, and the linear temperature and concentration fields of the components in the module for membranes of different thickness have been calculated from the experimental data using these equations.