I have the exact same situation described here: Multiple SSL Certificates in One Heroku Application, which is I want to securely access the same application using different domains.
The technique described in the first answer is promising, however I just discovered Heroku started a free service called Automated Certificate Management, which automatically takes care of creating and renewing certificates, which is great. But this is only available for applications with paid dynos.
I don't mind paying 7 $/month for a Hobby dyno, however as my app will only be used for SSL traffic, I don't know how to start a dyno without anything to run. In other words, I want to create a vacant dyno which won't do anything, just to activate the Automated Certificate Management. Is this possible and are there any thing that can go wrong in my plan?