Hi Dean,
Portal's temp directory can be relocated by the administrator via the portaladmin page.
go to /portaladmin/system/directories/temp and click the "edit" operation, replace the existing path with your new location (see https://developers.arcgis.com/rest/enterprise-administration/portal/edit-directory.htm)
BUT - the new path must still be a local directory for each Portal machine (not a network share) and the update wont create or populate the new folder - you need to do that first - on both machines in an HA site.
AND - - this will cause a Portal restart so not something to be taken lightly
the good news is that any files in the existing TEMP directory are really that - temporary - and do not need to be copied to the new location. In the same vein - I would suggest there is no reason not to delete any files in the temp directory that have not been auto-deleted - but maybe wait until they are a day old to ensure you are not impacting a running process.