I tried git show and git log, but these operate on the local repository and defined remotes. In order to see what git treeish your Heroku repo is using, try:
$ git ls-remote git@heroku.com:APP-NAME.git
97ec101adde21cfaf7f8c3ed47656e HEAD
97ec101adde21cfaf7f8c3ed47656e refs/heads/master
To find out the Heroku git repository name, you can also try
heroku info --app APP-NAME