Prominences and filaments are thought to arise as a consequence of a magnetized plasma undergoing thermal instability. Therefore, the thermal stability of a magnetized plasma is investigated under coronal conditions. The equilibrium structure of the plasma is approximated by a 1-D slab configuration. This is investigated in thermal instability taking into account optically thin plasma radiation and anisotropic thermal conduction. The thermal conduction perpendicular to the magnetic field is taken to be small but non-zero. The classic rigid wall boundary conditions which are often applied in the literature, either directly on the plasma or indirectly through some other medium, are replaced by a more physical situation in which the plasma column is placed in a low-density background stretching towards infinity. Results for a uniform equilibrium structure indicate the major effect of this change is on the eigenfunctions rather than on the growth rate. Essentially, perpendicular thermal conduction introduces field-aligned fine structure. It is also shown that in the presence of perpendicular thermal conduction, thermal instability in a slab model is only possible if the inner plasma has the shortest thermal instability time scale.