IR covers about 10 octaves of frequency, while the human visible spectrum covers only about 1 octave. At the end of far infrared, wavelengths are about 1 mm compared to the 3-9 mm of the human pupil. This strongly suggests that if a being/animal/robot senses this far IR, it would need eyes far larger than humans.
Human light reception require special light-sensitive molecules to move electrons about when light strikes them. Small chemical changes give us different types of receptors via gene duplication and historically preserved mutations. But there are reasons to suspect that from a common ancestor chemical it would be difficult to imagine historical branches that result in descendent chemical capable of 11 octaves of reception.
Human color perception weaves the signals from different types of receptors into a complex perception of hue, saturation, color. Some hues, the magentas and purples, are not present in the solar spectrum, because perception of them requires a signal high in low-frequency and high-frequency light. More color receptors would result in a hue-structure that is multi-dimensional. The spectral array of colors may be simply represented in a multi-dimensional hue perception space, or awkwardly represented in which case rainbows might be an acquired taste. Even if simply represented, it may not as visual stimulating as a hue progression in the "other" direction. More subtle effects are possible -- certain arrangements of green stripes could seem to clash horribly like purple and brown while a human sees a not-very-interesting wallpaper. With four or more types of primary visual perception, alien color sense is possibly very alien. Don't hire an alien to do interior design of your home, if you can avoid it.
With very large eyes and many different types of receptors, you might even get aliens who can see everything we do and pity use for being wholly blind, not just color blind, to a secret world of writing, signals, emanations, ghostly signs, luminous trails and self-illuminating rooms that noone should have to stub a toe in. For a sense of that, the CIE allows one to recolor pictures as if one was color-blind in a human fashion -- it's not something you would miss if you were born to it -- it's not something you would feel you lack unless you were constantly aware of those with greater perceptual gifts than your own. http://www.cs.ucf.edu/~yhu/grapp2006.pdf
Even with only three types of perceptual hue signals, seeing over multiple octaves, might create a similar perceptual color space with no way to guess what colors the others use. Apples and human blood might be both human-red and X-red, but limes and Earth's sky might by X-red and things they consider X-blue or X-green might be any color to us.