Heroku differs from traditional build & deploy by having the concept of "buildpacks", which are a generic method to identify, compile and package builds. The traditional method here would be to have hardcoded build commands, in a Makefile for instance. Buildpacks generally make custom build+deploy steps uneccessary, although one can specify custom buildpacks if necessary.
When notifying Heroku that a deploy is needed (usually by a Github webook), Heroku will run through all supported buildpacks until one can identify your app, which is then compiled and packaged by the buildpack. The output of this process is referred to as a "slug", which contains your app and all dependencies. For instance, a Python app would have the virtualenv packaged inside it. Heroku automatically deploys slugs that are built successfully.
This document describes a way to use LXC and existing third-party tools to reproduce this setup.
You need to have a server running that accepts webhooks and can take act