Is it possible to update Drupal page cache right after it is cleared?
Cache Warmer Module is the one you are looking for.


  cache_warmer is a drush command that hits a set of URIs of a drupal
  site based on the freshness of the content.


It is a drush integration for warming the caches using httprl, which means calls can be made parallely as well.

Since it is a drush extension you can tie it up easily with your cron as well.