Multisite missing tmp folder error while uploading

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As this sounds like an existing WordPress setup that ‘was’ working and now ‘is not’ working then check a couple of things:
1. have you recently moved server? or who else has changed anything on your server such as:
– file permissions for the WordPress folder – have these change?
– php.ini or .htaccess files – has anyone deleted these?
– server vhost or httpd.conf files – were these changed

I’d follow these instructions which I found from a quick Google on the error:

If you are receiving this error please follow these simple instructions below:

  1. Create a “tmp” folder in your WordPress root directory with 777 permissions. This can be done by your FTP program.

    1. Also create a “php.ini” file in same location.

  2. Add the following in php.ini file:

    upload_max_filesize = 16M
    upload_tmp_dir = on
    upload_tmp_dir = /home/username/public_html/wordpressDir/tmp

    Please make sure to replace username with your hosting username, and wordpressDir with the directory name of your WordPress install.
    If you have installed WordPress on your homepage then the path will be like: upload_tmp_dir = /home/username/public_html/tmp

  3. Copy the same php.ini file to your wp_admin folder.

source: FastWebHost