We show that a magnetic field can influence the proximity effect in NS junctions via diamagnetic screening current flowing in the superconductor. Using ballistic quasi-one-dimensional (Q1D) electron channels as an example, we show that the supercurrent flow shifts the proximity-induced minigap in the excitation spectrum of a Q1D system from the Fermi level to higher quasiparticle energies. Thermal conductance of a Q1D channel (normalized by that of a normal Q1D ballistic system) is predicted to manifest such a spectral feature as a nonmonotonic behavior at temperatures corresponding to the energy of excitation into the gapful part of the spectrum.