not tested config

.gitignore

@@ -0,0 +1,3 @@
+/venv
+.idea
+/postgres

Dockerfile

@@ -0,0 +1,7 @@
+FROM gitea/gitea:1.14.5-rootless
+
+RUN mkdir -p /data/gitea
+
+EXPOSE 3000
+
+CMD ["/usr/bin/gitea", "web"]

heroku.yml

@@ -10,3 +10,6 @@ setup:
 build:
   docker:
     web: Dockerfile
+
+run:
+  web: ./start.sh

run.sh

@@ -0,0 +1,23 @@
+#!/bin/bash
+
+export DB_HOST=$(heroku config:get DATABASE_URL | sed 's/.*\/\/\(.*\):\(.*\)\/.*/\1/')
+export DB_USER=$(heroku config:get DATABASE_URL | sed 's/.*\/\/\(.*\):\(.*\)\/.*/\1/')
+export DB_PASSWORD=$(heroku config:get DATABASE_URL | sed 's/.*:\/\/.*:\(.*\)@.*/\1/')
+export DB_NAME=$(heroku config:get DATABASE_URL | sed 's/.*\/\(.*\)/\1/')
+
+cat > /data/gitea/conf/app.ini <<EOL
+[database]
+DB_TYPE  = postgres
+HOST     = ${DB_HOST}
+NAME     = ${DB_NAME}
+USER     = ${DB_USER}
+PASSWD   = ${DB_PASSWORD}
+SSL_MODE = require
+
+[server]
+DOMAIN   = ${HEROKU_APP_DEFAULT_DOMAIN_NAME}
+HTTP_PORT = ${PORT}
+
+EOL
+
+/usr/bin/gitea web