A "pure intelligence" is something an intelligence that is only intelligence a mind without extra bits. What exactly constitutes "extra bits" stuff that is not absolutely necessary to the existence of a mind is certainly not something anyone can offer a definitive answer on. Clearly no human could ever be a pure intelligence because we have a bunch of extra stuff which we cannot go without our bodies for instance. Whether or not emotions are necessarily part of a pure intelligence I don't know. They cannot be easily be dismissed since emotions in large part are the motivational force behind human actions and one might argue that computation without motivation cannot be intelligence.
Perhaps such a thing as a "pure intelligence" cannot, even in principle, exist. After all every intelligence must have some physical basis in order to have a place in our universe so even a computer intelligence must have a "body" in some sense and therefore have some aspects of its existence which are not essential to what really makes a mind. When I say that humans cannot be pure intelligences because we have bodies I do not mean that having a physical shell is what makes our intelligence less than "pure". What I mean is that our bodies motivate us in ways that are outside of what is essential to our intelligence. One might argue that self preservation and reproductive urges could be essential consequences of real intelligence (though personally I find that hard to believe) but clearly many things that are important to human beings are simply visceral in their nature and nothing more. While sex might have the benefit of reproduction and one could eve say that there can exist a purely intellectual interest in it, people do not engage in sex primarily as an intellectual activity. This is generally true of a great many pass times snowboarding for instance is in part an intellectual activity (plotting your course and avoiding trees etc) but this is only a secondary reason why the activity is fun, the actual physical sensation is tremendously important to the activity.
Saying that this means that a pure intelligence can't have outside stimuli is perhaps going a bit too far. One could imagine a very powerful intelligence simulating an external world and a lesser intelligence interacting with it. One could of course say that the simulated intelligence is then not pure and the greater one because it is self contained is but the distinction is unnecessary in my opinion. Furthermore I am not willing to rob a pure intelligence of the ability to dream or imagine.
Human beings were not made for thinking but for hunting and surviving. Hunting in particular requires pattern recognition, planning and flexibility. Survival requires adaptability either in the form of adapting to ones environment or adapting ones environment to suit ones self. Adapting requires creativity you need to be able to understand your environment and imagine a way to change either yourself or the environment. The combination of pattern recognition and imagination with a sufficiently interesting database is probably sufficient for "intelligence".
Whatever the qualities necessary for intelligence human beings are not terribly good at them. We recognize patterns most readily that would have helped in tracking down food and other patterns that proved useful to our survival. Obviously not every pattern that humans are good at recognizing falls into this narrow view but I imagine a disturbingly large portion of them do. Because all of this overhead of pattern recognition and imagination comes at a cost of energy and development it wouldn't make sense for evolution to make us too good at it. Our brains already take up a large amount of the energy our bodies produce and when it comes to tracking prey once you can tell how a rabit is going to run there is no point to further increasing the power of the ability further and further.
Ultimately I find it rather annoying the degree to which things that are essential parts of who I am are not essential to what constitutes my "intelligence". I admit to being a visceral being. I like sunsets and not because they are interesting or elegant but just because I like to look at them. I like being warm and the way that I seek physical comfort from others and what kinds of ice cream I like are parts of me that are not important ultimately to what really makes my mind but they can be important to what makes me who I am. Sometimes I wish I could divorce myself from the physical aspects of myself and exist as a pure intelligence. More often I think that I would like to deepen my physical experience and experience more. I want to know what it is like to be human in the most general sense. I want to grow old and I want to be depressed and happy and I wish I could be female as well as male at some point (somehow I doubt I am alone in that). I want to know what it is like to be bald and to have long hair I want to break some bones sometime just to know what it is like. This deeply visceral aspect of my nature puzzles me but I suspect that it is an important part of what it means to be the semi-pure intelligence that is human.