Cache warming for logged in user roles
You can use drush user-login together with curl (or wget) like this:

drush --uri=http://your-site.com/drupal-dir-if-any/ user-login --browser=0 username path/to/heavy/site | xargs curl -L


The drush user-login command prints a one-time login link of the following form:

http://your-site.com/drupal-dir-if-any/user/reset/1/1390809497/hzqAmTzHMdBIXDIrkbDsmLIyPQtcDnjAufz9Fd5OUJk/login?destination=path/to/heavy/site


Then xargs will pick it up from stdin and passes it as last command line argument to curl. Finally the -L flag instructs curl to follow redirects. You might want to also supply -o /dev/null in order to discard the output of curl.