You need to check your file/folder permissions. Your webhost may have them set too strictly for WordPress to write its own temp folders and extract its own archive in /wp-content/upgrade/. See Changing File Permissions « WordPress Codex:
Typically, all files should be owned by your user (ftp) account on your web server, and should be writable by that account. On shared hosts, files should never be owned by the webserver process itself (sometimes this is www, or apache, or nobody user).
Any file that needs write access from WordPress should be owned or group-owned by the user account used by the WordPress (which may be different than the server account). For example, you may have a user account that lets you FTP files back and forth to your server, but your server itself may run using a separate user, in a separate usergroup, such as dhapache or nobody. If WordPress is running as the FTP account, that account needs to have write access, i.e., be the owner of the files, or belong to a group that has write access. In the latter case, that would mean permissions are set more permissively than default (for example, 775 rather than 755 for folders, and 664 instead of 644).
Or, try a manual upgrade; all that involves is uploading a few folders and core files (and not overwriting wp-content and wp-config.php). See http://codex.wordpress.org/Updating_WordPress#Manual_Update