I have a CNAME for www.mywebsite.com pointing towards example.herokuapp.com, and the original Heroku page is working just fine. However the CNAMEd website (www.mywebsite.com) is showing a Herokuapp 404. Why is this so? Why can't I point my CNAME towards the Heroku page properly?
You can't just set a CNAME and hope for the best when it comes to Heroku. You actually need to log into the Heroku admin panel and configure the CNAME record that you are creating so that Heroku knows what CNAME'ed domain maps to what app on the server.