Context and Page Caching
If you have access to your ssh console, you can use cron

crontab -e


Then you put inside, at the bottom:

PATH=/usr/local/sbin:/usr/local/bin:/sbin:/bin:/usr/sbin:/usr/bin
0 14 * * * cd /var/www/drupal &amp;&amp; drush cc all


the above will clear the cache with drush everyday at 2pm.  

A few notes: 


replace cd /var/www/drupal with the actual path to your drupal.
I believe the default runs at UTC time.
You need to install drush if you haven't already.


An alternative to using Drush, you could create a PHP or Python or NodeJS etc.. file that uses mysql to delete the row that holds the page cache in your DB, and run the file with cron at 2pm.