Push from github to heroku without downloading repo

You can't push straight from Github to Heroku.

You're going to have to use the third host to coordinate the push. This could be fired from a Github post-receive hook.

To sync straight across use something like:

git remote add github [email protected]:user/repo.git
git remote add heroku [email protected]:app.git

git push heroku refs/remotes/github/master:refs/heads/master

Codeship.io does this as a service now, and automatically configures the appropriate git webhooks on public or private github repos.

There are a few other "continuous integration as a service" (CIAAS) options out there, but in general they get around the problem you're specifically presenting: web hooks need to hit a 3rd-party service, which in turn can trigger the heroku build process.

These CIAAS hosts act as the 3rd-party, and usually offer a free tier for public projects. You can also roll your own by deploying a web hook receiving server, which can both pull and push git repos.