I've always wanted to know if he can see while he's using his heat vision, and if he can, what does it look like, is everything red, does his vision spectrum change?
Have we ever seen through his eyes while he was using his heat vision?
According to the Superman Wiki page, and more generally, the heat vision page on the Superpower Wiki, heat vision doesn't actually affect one's vision per-se - it is more that it is heat rays coming from the eyes (hence the misnomer 'Heat vision').
However, the below quote form the aforementioned Superman Wiki page explains that:
[Heat vision] was originally considered to be a subset of X-Ray Vision; for example, Superman was known to melt metal with "The heat of his X-Ray vision". As his powers developed and became more defined, however, Heat Vision became distinguished as an individual power.
The ability of heat vision being part of X-Ray vision was introduced in Superman (vol. 1) #59 (July 1949), and later established as a separate power in Action Comics #275 (April 1961) (Source).
The below comic (Superman #38) shows the origin of the heat vision in the form of a 'solar flare':
Hence my title of 'it depends' - originally, heat vision, being a feature of X-Ray vision meant that he would be viewing the world in X-Ray vision rather than normally, but *once heat vision became a distinct power*, it seems there is no change to Superman's vision.