Dear Duncan,
The .tmp file automatically created when you are working with Outlook. It is just a copy of PST file which stores data temporary. In case your outlook got crashed due to any error then it is possible that you may lose the data saved in .tmp and .pst file. Your PST file shows 0 bit data size it means your data is completely lost form PST file. So there is no chance to recover email from PST file.
But if you are working with Exchange Server, than you have option to recover email from OST file So try to find OST file at this location:
Windows 7 and Windows Vista drive:\Users\user\AppData\Local\Microsoft\Outlook
Windows XP drive:\Documents and Settings\user\Local Settings\Application Data\Microsoft\Outlook
Now if you have found OST file than it is very easy to recover your email back from the OST file with the help of Stellar Phoenix Convert OST to PST Software, It helps to convert OST file data into PST file and you can easily access the PST file data from your Outlook. You cannot directly import OST file data through Outlook so It is necessary to convert OST to PST so that you can import the data easily.
http://www.stellarinfo.com/exchange-ost-recovery.htm Hope you will find this solution perfect to resolve your problem.