I seem to remember reading back in the day that Byrne's version codified the idea of Kryptonian cells storing energy from sunlight. I thought it followed that heat vision was a means of directing that stored energy through the eyes.
It could have something to do with the solar cell idea but Byrne was adamant, at least initially, the Superman didn't shoot rays from his eyes. In the early issues of the reboot, heat vision was drawn as a flash in his eyes and then the image of something melting.