Update from 3.6.x to 3.6.3 Timeout
From Joomla! Documentation
Timeout problems if you update.
This pertains only to Joomla! version(s): 3.6.x
What is the cause
As we have implemented a reinstall feature in 3.6.0 we always need the complete (bigger) `Joomla_3.6.x-Stable-Update_Package.zip` package on the update server. With some servers this may result in timeouts on updating / downloading the update package.
How to fix
If you have such a site please use the table below to find the correct package.
There is a PR to differ between a update and a reinstall: https://github.com/joomla/joomla-cms/pull/11497 as long as this is not merged we need to use this workaround on sites that time out when using the full package.