Assumtions: Git repo cloned from remote named "production" (hence the "-r production" flags)
Pane 1:
heroku logs -t -r production
Pane 2:
heroku maintenance:on -r production
heroku ps:scale web=0 -r production
Watch the logs in Pane 1 and make sure requests stop coming in
heroku run rake db:migrate -r production
Make sure everything went well (no errors in either pane)
heroku ps:scale web=2 -r production
Watch the logs in Pane 1 until both apps have started
heroku maintenance:off -r production