The previous 2 Heroku application stacks came with a Varnish layer which automatically reverse-proxy-cached content based on http headers.
The new Heroku cedar stack doe
A more modern answer, with 20/20 hindsight:
To get the caching performance approaching that of bamboo on cedar-14, this is the usual pattern:
I would recommend redis-rails as a rack cache backend, if you're doing caching at multiple layers (FE (CF/FY), page, action, fragment, etc.).