This command does it for everything Sent after 9/22/2016 and before 9/27/2016. You’ll then have to export it from the temporary_storage_mailbox, and import it into original_mailbox.
This is all one command line in Exchange PowerShell, set as multiple lines for easy reading. The SearchQuery is especially arcane; there is a lot of incorrect syntax out there for it, the below worked today (2016-09-27) on Exchange 2010 fully updated.
Search-Mailbox -Identity original_mailbox@domain.com
-TargetMailbox temporary_storage_mailbox@domain.com
-TargetFolder "Rescued_From_Dumpster"
-SearchQuery {Sent:>22-Sep-2016 AND Sent:<27-Sep-2016}
-SearchDumpsterOnly