Message: "CiviCRM does not have permission to write temp files" after login into back-end Joomla
They may have changed how they're running PHP for your hosting, which could lead to your old templates_c files being unwritable to the new PHP process.

As Lobo's comment advises, removing the files and ensuring that the templates_c is world-writable should resolve the permission issue.

It'd be ideal if templates_c belongs and is writable only to the new PHP process.