Gapped excitation spectra of Andreev states in one- and two-dimensional normal systems in contacts with superconductors are analyzed in the presence of a parallel magnetic field. It is shown that in the ballistic regime there is a specific interplay between magnetic field spin splitting and the effect of a proximity-induced screening supercurrent which preserves time-reversal symmetry for certain groups of Andreev states. In this case the thermal conductance of the system remains suppressed well below the normal-state value in a rather wide range of magnetic fields approaching the critical fields of the superconductor. (C) 2004 Elsevier B.V. All rights reserved.