What Causes the Whole Tooth to Turn Black Under a Temporary Crown?

You should return to the dentist to have the temporary checked as it is not sealed well.  Leaving the temp with the black stain could lead to a lot of sensitivity on that tooth once the final restoration is seated.  The black stain can be removed from the tooth with pumice and peroxide by the dentist

This is not so unusual. When the temporary crown leaks, it happens. Tooth can usually be returned to its original color by polishing with a mixyure of dental pumice and hydrogen peroxide. Not to worry!

This is usually due to leakage of saliva under the crown - it can be cleaned with peroxide and a brush and is of little consequence as long as the tooth isn't sensitive. 

There are billions of bacteria that live in the mouth and sometimes the conditions are just right that they will get under a temporary and turn it black.  It is the bacteria that cause this and it can be cleaned off by brushing peroxide on the tooth.  It doesn't do any damage, but if it is in front it can hinder the looks of the crown.  Hope that helps!

Actually this is not uncommon.  Somehow your temporary crown loosened up a bit, probably from chewing on it, and this allowed a microscopic space for bacteria and fungi to set up residence under the temporary crown.

When the dentist took of the temporary crown there might have been an annoying odor and the tooth would have appeared black.  It is often times known as "black scuz" to dentists (not a technical name).

The black scuz and odor can easily be removed in about three seconds by bathing the tooth with regular old hydrogen peroxide solution.  No harm, no foul.  No permanent damage either.