Kevin Warwick had a sonar sense implanted and could sense whether an object was close or far. Evidence is accumulating that our brains can make sense of "foreign" information like sonar (consider the vOICe).
It can be assumed/hoped that artificial eyes will feed the human brain information more than the currently available spectrum (into the visual sense, not through the sense of warmth).
Infrared via carotine diet
There possibly were army experiments to extend the human spectrum into the realm of infrared by maintaining a special carotine diet, but they were abandoned) when technological advances made seeing infrared easier.
Ultraviolet in aphakic patients - edited in
Some people with cataracts have their lense removed (resulting in aphakia), reportedly leading to UV vision.
The eye represents a compromise between clear focus and breadth of spectrum. What does ultraviolet look like? Prof Stark possesses UV vision because he is aphakic in one eye and, with Professor Karel Tan, has published research on the nearest visible equivalent. His conclusion is that it looks whitish blue or, for some wavelengths, a whitish violet.
A thought experiment with an extended visible spectrum seems interesting to me. It touches both on the qualia debate and cognitive science. I still hope you won't vote this off-topic, because I don't think cognitive science has the answer concerning the subjective experience of the stretched spectrum.
I can think of two main possibilities.
for reference the current (most common) human visible spectrum with wavelengths as objective baseline (from Wikimedia)
1. Our current repertoire of colors is stretched.
2. We see new colors.
Has this been debated in the literature? What is being proposed? Are (1) and (2) actually the same (more acuity = more colors)?
I think there is no expectation implicit in language (infrared and ultraviolet), but still when people want to demonstrate heat vision they often use red color and, um, well I don't know any movies about superheros with bee vision.