Heroku wouldn't necessarily be the issue here - it's an environment which allows your app to run (on Amazon EC2 I think)
Multi-Threaded Servers
The thing you've got to look for is the server software you use to run your app. Heroku basically takes your server gem & allows it to run with their processors, and other computing power; so it's really whether their platform can play ball with the right server
You're really looking for multi-threaded servers, which you can find here Is puma the ONLY multi-threaded rails 4 http server?
Puma
Rainbows! supports multiple concurrency models, including multithreading
Zbatery - Rack HTTP server without a fork stuck in it
Phusion Passenger 4 has supported multithreading since its beta stages
Thin does have a threaded mode which can be enabled by passing
--threaded or by setting threaded: true in the appropriate configuration file (e.g. bundle exec thin start --threaded)
Net::HTTP::Server, despite the lack of advertising, supports
multithreading; very minimalist