A thermally-assisted recording (TAR) disk drive uses “shingled” recording and a rectangular waveguide as a “wide-area” heat source. The waveguide generates a generally elliptically-shaped optical spot that heats an area of the recording layer extending across multiple data tracks. The waveguide core has an aspect ratio (cross-track width to along-the track thickness) that achieves the desired size of the heated area while locating the peak optical intensity close to the trailing edge of the write pole tip where writing occurs. The large cross-track width of the waveguide core increases the volume of recording layer heated by the optical spot, which reduces the rate of cooling. This moves the peak temperature point of the heated area closer to the write pole tip and reduces the temperature drop between the peak temperature and the temperature at the trailing edge of the write pole tip where writing occurs.