While downloading, TB stores its messages in the temp folder. Only when the message has been downloaded completely will it be imported into the message base.

What happens here is that TB can't store the message in your temp folder, so the importing into the message base won't happen either.
This can have the following causes:
1) You don't have the rights to write in your own temp folder. This isn't very likely as it means that you've got a very screwed Windows setup and TB isn't the only program that uses the temp folder. So you should have problems all around.
2) The drive with your temp folder on it is full. As it probably is your system drive too this would cause major problems, but you could look whether your temp folder is next to empty (as it should be) and whether there is an excessive number of bat????.tmp files. (Even with TB running I've got none of them.) The easiest way to view your temp folder is via Windows start button:
Start -> Run as -> %temp%
This starts an Explorer screen in your temp folder and you can delete all files and folders in your temp folder (not the temp folder itself)
Note that a lot of bat????.tmp files means that TB is acting sluggish too.
3) A program is keeping TB to write a specific file to the temp folder. The most likely case is a virus scanner (virus message) or maybe a firewall (some firewalls (or content scanning programs) don't allow some types of attachments)
The best way to solve this problem is to view the messages on your server with either TB's mail dispatcher (Account -> Dispatch Mail On Server -> All messages) or with your ISP's webmail interface and find the problematic message and delete it on the server. Note that TB's mail dispatcher is safer than a webmail interface, because some viruses are executed just by viewing it in your browser.
When both of these options are a tad bothersome because your keeping 30 or 60 days worth of mail on your server you can also do this:
Disable your virus scanner
Collect your mail
Check the new messages you've got
Delete any suspected messages
Purge the folder you've found these message and purge your inbox too.
Empty your Trash (and purge that too)
Enable your virus scanner
While you're busy doing this, you shouldn't do any high risk activities like surfing the net, dowloading files, inserting media in your computer, etc.

The most likely cause is number three, but when it happens one of the symptoms often is an excessive of bat????.tmp files in your temp folder.