When ever you run into an issue where you think you're out of diskspace or you're running out of diskspace there are 2 commands you can run to confirm this. 
NOTE: Be aware that in addition to running out of diskspace, you might also be running out of inodes.
df
The command df is the venerable tool for reporting on filesystem usage.
Example
It has 2 switches that you'll likely use most of the time. Either -h or -k. I always opt for -h since this shows the disk space in human readable units.
$ df -h
Filesystem                         Size  Used Avail Use% Mounted on
/dev/mapper/fedora_greeneggs-root   50G   11G   36G  23% /
devtmpfs                           3.8G     0  3.8G   0% /dev
tmpfs                              3.9G  2.3M  3.8G   1% /dev/shm
tmpfs                              3.9G 1016K  3.8G   1% /run
tmpfs                              3.9G     0  3.9G   0% /sys/fs/cgroup
tmpfs                              3.9G  1.1G  2.8G  27% /tmp
/dev/sda1                          477M  101M  348M  23% /boot
/dev/mapper/fedora_greeneggs-home  402G  146G  236G  39% /home
Notice that my /tmp is configured with 3.9GB or which 1.1GB is used.
tune2fs
This command is a bit more obscure but is useful when you want to confirm if your system if running out of inodes. Believe it or not, but inodes is a limited resource that you allocate during the creation phase of your filesystem. Once allocated it cannot be changed.
I'd check to see if your system has run out of inodes.
Example
$ sudo tune2fs -l /dev/mapper/fedora_greeneggs-root | grep -i "inode"
Filesystem features:      has_journal ext_attr resize_inode dir_index filetype needs_recovery extent flex_bg sparse_super large_file huge_file uninit_bg dir_nlink extra_isize
Inode count:              3276800
Free inodes:              3060507
Inodes per group:         8192
Inode blocks per group:   512
First inode:              11
Inode size:           256
Journal inode:            8
First orphan inode:       1321314
Journal backup:           inode blocks
So with the above you'll notice that we have 3276800 inode of which 3060507 are available.
Alternative inode method
There are several other ways you can do this. Certain versions of the df command can also report inodes.
$ df -i
Filesystem                          Inodes  IUsed    IFree IUse% Mounted on
/dev/mapper/fedora_greeneggs-root  3276800 226065  3050735    7% /
devtmpfs                            994457    480   993977    1% /dev
tmpfs                               996186     19   996167    1% /dev/shm
tmpfs                               996186    623   995563    1% /run
tmpfs                               996186     12   996174    1% /sys/fs/cgroup
tmpfs                               996186    230   995956    1% /tmp
/dev/sda1                           128016    320   127696    1% /boot
/dev/mapper/fedora_greeneggs-home 26722304 908502 25813802    4% /home
     
    
df -h(storage space),cat /etc/fstab(to see your/tmpmounting), andstat -c%a / /tmp(permissions for/and/tmp).# df -h df: cannot read table of mounted file systems