That's very strange. We've never seen that before, and 3.1.2 has been installed hundreds of times.
My best suggestion is to try unzipping the whole component to a directory on your server (like /var/www/html/joomla/tmp) and then using the "Install from Directory" option from the Install/Uninstall screen. Hopefully that will fix the issue, but if it doesn't (and it says a file doesn't exists) you should be able to very quickly verify that the file is indeed there.
Finally, please make sure that you're running Joomla 1.5, and that the /components and /tmp directories are writeable. You can see this if you go to Help->System Info and click the Directory Permissions tab.
If that doesn't help, let us know and we'll see what more we can do.