Black tooth under temp crown, is it tooth decay?

It All Depends. All other answers are valid. However, I'd like to add that if the temp crown was recently placed while you're waiting for a permanent crown, the black coloration can be from bacteria getting through the temp crown. It's a result of not having a good seal with the temp crown and usually not a cavity. You commonly see this if the temp crown has been in place for some time where the seal is bad.
Maybe. Could be decay, or stain from a metallic (amalgam) filling that was in the tooth previously, or if the tooth has a root canal, the tooth can turn dark over time.
Maybe also. It could also be from trauma which can cause discoloration.
Temp not sealed. When the temporary crown leaks, the black stain can be appeared on the dentin. It will be removed from the tooth with pumice and peroxide by the dentist before final restoration.
Black tooth. Was it black all along? ask your dentist, he/she will have insight... a lot of good suggestions were made by other respondents..
Maybe. If the temporary crown has been on your tooth for a long time (months) it could be decay. If the temp has just bee placed it could be dark tooth structure or it might just be shadow from the opaque temporary cement.