Run a reverse ssl termination proxy using nginx on Heroku so that you can use a custom domain with Intercom in the simpliest possible way. Yes, you still need to setup the SSL but Heroku's ACM makes that easy and you'll need a CNAME/ALIAS record but still, this is much easier than mucking around.
CUSTOM_DOMAIN- should be your domain (no scheme) that you set in the Intercom Help Center Settings. Eg. support.yourdomain.com
Updated to heroku-16 stack and recent community build pack for nginx.
Based on funwhilelost/heroku-reverse-proxy who at least had something that wasn't based on cedar.