When pivotaltracker switched into a paying scheme, I decided to try Redmine on Heroku. It took more time than I expected and I wanted to share some important points that might help people, who would like to try the same configuration.
This might be far from being a complete guide because I didn’t take note of the whole process, I will do that next time

Heroku documentation describes the overall process well. Heroku recommends installing gems using the Bundler application. But this caused problems with the redmine version 1.1.1 that I used. Heroku logs were displaying “Missing the Rails 2.3.5 gem”, “H10 – App crashed” errors.

Instead I defined my gems using the gem manifest file: .gems. Gems that I used and their versions that worked for me were:
builder (2.1.2), rails (2.3.5), rack (1.0.1), i18n (0.4.2)

Here is a discussion that contains the information that Rack 1.1.0 is incompatible with Rails 2.3.5 and older, and here is another one where using the 1.0.1 version is suggested.

I removed redmine’s vendor/rails directory in order to allow Heroku to manage the gems.

Also I added the following line to config/environment.rb file:
config.action_controller.session = { :key => "_myapp_session", :secret => "longStringOfCharacters" }

I believe newer versions of redmine will allow using the gem bundler and newer gem versions.