Deleting content of /private/tmp moved on different HDD
After doing some research, I ended up writing a shell script and using launchd to have it execute at boot time.

The script I use (/usr/local/bin/empty-tmp.sh) :

#!/bin/bash

# Delete files (other than directories) that haven't been modified in more than 1 day
find /Volumes/MacintosHD/private/tmp -not -type d -ctime +1d -delete

# Delete empty directores that have been created more than 1 day ago
find /Volumes/MacintoshHD/private/tmp -d -type d -empty -mindepth 1 -Btime +1d -delete


and the property list (in /Library/LaunchDeamons) :

&lt;?xml version="1.0" encoding="UTF-8"?&gt;
&lt;!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd"&gt;
&lt;plist version="1.0"&gt;
&lt;dict&gt;
  &lt;key&gt;Label&lt;/key&gt;
  &lt;string&gt;com.samric.emptytmp&lt;/string&gt;

  &lt;key&gt;ProgramArguments&lt;/key&gt;
  &lt;array&gt;
    &lt;string&gt;/bin/bash&lt;/string&gt;
    &lt;string&gt;-c&lt;/string&gt;
    &lt;string&gt;/bin/wait4path /Volumes/MacintoshHD/private/tmp/ &amp;&amp; /usr/local/bin/empty-tmp.sh&lt;/string&gt;
  &lt;/array&gt;

  &lt;key&gt;RunAtLoad&lt;/key&gt;
  &lt;true/&gt;

  &lt;key&gt;LaunchOnlyOnce&lt;/key&gt;
  &lt;true/&gt;
  &lt;/dict&gt;
&lt;/plist&gt;


Now the key is using wait4path to make sure the secondary HD (MacintoshHD) is properly mounted before invoking the script.  Failing to do so will result is the script not deleting any files since they won't be accessible.