Question

What mental process is one that is just outside our conscious thinking, but can become conscious at any time?

Answer 1

The unconscious mind is still viewed by many psychological scientists as the shadow of a “real” conscious mind, though there now exists substantial evidence that the unconscious is not identifiably less flexible, complex, controlling, deliberative, or action-oriented than is its counterpart. This “conscious-centric” bias is due in part to the operational definition within cognitive psychology that equates unconscious with subliminal. We review the evidence challenging this restricted view of the unconscious emerging from contemporary social cognition research, which has traditionally defined the unconscious in terms of its unintentional nature; this research has demonstrated the existence of several independent unconscious behavioral guidance systems: perceptual, evaluative, and motivational. From this perspective, it is concluded that in both phylogeny and ontogeny, actions of an unconscious mind precede the arrival of a conscious mind—that action precedes reflection.

Answer 2

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2440575/

Answer 3

Or, you could just say "preconscious" :P
What did you eat for breakfast? Chances are, you weren't consciously thinking about that until you read the question. If you can easily bring it to your mind, it is part of your preconscious.

Answer 4

R.I.P Cheyenne.

Answer 5

Mental process, you might be very conscious about how you'd like some candies, but you can't help but to eat some candies >_> because you are a biological robot, consciousness is likely something all animals have, within limits.