No Trash can typically handle anything. The problem is likely more that your userid does not have permissions to move these particular files and/or directories from /var/tmp
.
To confirm drop to a shell and cd /var/tmp
and check who the owner is of these files as well as the permissions on these files.
$ ls -la /var/tmp
Example
$ ls -la
total 216
drwxrwxrwt. 8 root root 4096 Feb 6 09:38 .
drwxr-xr-x. 24 root root 4096 Jan 7 02:20 ..
drwxr-xr-x. 2 abrt abrt 4096 Feb 5 12:27 abrt
-rw-r--r--. 1 root root 0 Jan 13 13:49 ipp_class.log
-rw-r--r--. 1 root root 0 Jan 13 13:49 ipp_driver.log
-rw-r--r--. 1 root root 0 Jan 13 13:49 ipp_job.log
-rw-r--r--. 1 root root 0 Jan 13 13:49 ipp_printer.log
-rw-r--r--. 1 root root 53 Jan 13 13:49 ipp_request.log
drwx------. 2 saml saml 4096 Dec 31 1969 orbit-saml
-rw-------. 1 saml saml 20480 Jan 30 00:47 .swo
-rw-------. 1 saml saml 20480 Jan 30 00:46 .swp
drwx------. 3 root root 4096 Feb 5 12:09 systemd-private-dxtLOx
drwx------. 3 root root 4096 Feb 5 12:09 systemd-private-HGWviW
drwx------. 3 root root 4096 Feb 5 12:09 systemd-private-Sga875
-rw-------. 1 root root 65816 Jan 15 17:49 wireshark_pcapng_wlp3s0_20140115174932_AX9520
-rw-------. 1 root root 4056 Jan 15 17:49 wireshark_pcapng_wlp3s0_20140115174942_BrNwdN
-rw-------. 1 root root 30732 Jan 15 17:50 wireshark_pcapng_wlp3s0_20140115174958_Un8VJu
-rw-------. 1 root root 13392 Jan 15 17:56 wireshark_pcapng_wlp3s0_20140115175604_Oyz8JT
So if I were user saml
when I ran Thunar or Nautilus and attempted touch any of the files owned by root
I wouldn't be allowed to do so, in the above example.
But what user am I?
If you're in a shell and don't know what username you are (don't laugh, it happens) you can use the command:
$ who am i
saml pts/11 2014-02-06 09:04 (:0)