Seems like I had to run heroku ps:scale web=1
to get it working properly. This is strange because I am 100% sure I started other Heroku projects before and I didn't have to run that command in order to see my application working in http://my_project.herokuapp.com.
My Procfile looked like this when it ran successfully:
web: cd my_project; gunicorn my_project.wsgi --settings=my_project.settings.production
Edit
I previously ran gunicorn with the -w 1
option:
web: cd my_project; gunicorn my_project.wsgi -w 1 --settings=my_project.settings.production
That probably activated a dyno.