It is shown by theoretical arguments that thermally-assisted recording using conventional optical means for heating the medium locally gives only moderate improvements over conventional recording. These improvements are comparable with those of perpendicular recording over oriented longitudinal recording. When bits are cooled down immediately after writing and not heated again, large improvements in areal density and signal-to-noise ratio are possible. However, writing becomes extremely difficult in the region of small switching times where thermally-assisted recording allows large grainsize reductions.