It’s now possible to try the Heroku feature Roberto wrote about in his answer, without contacting Heroku. It’s called Heroku Labs: Dyno Metadata and you can enable it by
heroku labs:enable runtime-dyno-metadata -a <app name>
and then the information is available (on the next deploy) as environment variables:
~ $ env
HEROKU_APP_ID: 9daa2797-e49b-4624-932f-ec3f9688e3da
HEROKU_APP_NAME: example-app
HEROKU_DYNO_ID: 1vac4117-c29f-4312-521e-ba4d8638c1ac
HEROKU_RELEASE_VERSION: v42
HEROKU_SLUG_COMMIT: 2c3a0b24069af49b3de35b8e8c26765c1dba9ff0
HEROKU_SLUG_DESCRIPTION: Deploy 2c3a0b2
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