Implementation of "Remember me" in a Rails application

My Rails-app has a sign in box with a "remember me" checkbox. Users who check that box should remain logged in even after closing their browser. I'm keeping track of whether users are logged in by storing their id in the user's session.

But sessions are implemented in Rails as session cookies, which are not persistent. I can make them persistent:

class ApplicationController < ActionController::Base
  before_filter :update_session_expiration_date

  private

  def update_session_expiration_date
    options = ActionController::Base.session_options
    unless options[:session_expires]
      options[:session_expires] = 1.year.from_now
    end
  end
end

But that seems like a hack, which is surprising for such common functionality. Is there any better way?

Edit

Gareth's answer is pretty good, but I would still like an answer from someone familiar with Rails 2 (because of it's unique CookieSessionStore).