Word for unconscious vital process?

Autonomic.

The nearest thing I can think of is "tacit knowledge", which I don't think applies to the example of the heart, per se, but it does refer to things we know but don't know how we know them. Knowledge, skills etc that we take for granted without ever having consciously arrived at them.

It's related to what you're describing, but not identical.

http://www.artsci.wustl.edu/~philos/MindDict/tacitknowledge.html

Didn't see amo's response before I wrote mine, but that answer was probably what you were looking for.

By the way, an excellent resource for finding words is the One Look Reverse Dictionary. You type in the definition and it finds words that might fit.

onelook.com/reverse-dictionary.shtml

For instance, I typed in and it gave me AUTOMATISM. Definition is: any reaction that occurs automatically without conscious thought or reflection (especially the undirected behavior seen in psychomotor epilepsy).

I think you might also use "involuntary."

Or maybe "reflex" ?

Look in Wikipedia under autonomic nervous system. I think this is what you're loking for...

The term I remember most being used ("way back" in school, as well as other contexts) is "involuntary"; this never quite sits right with me though, as there is the implication of being "contrary to volition" - which is certainly not [usually] the case with most such functions/processes.

I have a similar issue with "autonomous", as that seems to imply "beyond control" - and in fact, most such functions/processes are controlable to some degree (e.g. I've discovered I have the somewhat unusual ability to consciously affect my pupil dialation).

"Reflexive" is also a suitable candidate, although that carries the implication of a reaction, and often the original stimulus is far enough removed (or continuous enough) from the subsequent process as to seem virtually unrelated.

However, in spite of implications I "feel" with these words, they are the most commonly used terms, and ultimately that seems the best indication of "correct" usage of language. Truth told, whenever discussing such matters I wrestle with which word to use, and will often "offer" more than one; sometimes I will also use "unconscious", which seems quite accurate to me and without the "contrary implications" of these other words - something controlled by the nervous system usually without conscious thought, yet not entirely isolated therefrom. (Note I do lean towards the more Jungian "unconscious" rather than a Freudian "subconscious" - but that's another discussion entirely ; )

Autonomic

Jake, you discounted autonomous but autonomic is somehwat different. Autonomic specifically refers to the autonomic nervous system which governs heart rate, breathing, etc., things under unconscious control, but may sometimes be consciously overridden. So, as has already been said, autonomic seems to be the perfect word.