Indeed - that's how UCB Systems worked. /tmp was a small scratch disk and anything there was suspect. Scratch files were not a CShell feature, they were a UNIX feature, very much needed on the 16-bit address PDP-11 where it was developed.
The idea originally became popular with Dennis's C Compiler which used it for the intermediate files between the passes on the PDP-11. On a large public system like a University, /tmp would fill with cruft. It was traditionally removed on reboot. But that was not good enough for production systems that did not reboot.
My memory is that there was a script that was similar to what Aharon suggested that ran in the early hours of the day, although before it ran it created a time_stamp_file with touch(1) set to be 6 hours previous so the script let anything under 6 hours survive using a negation on the -newer time_stamp_file clause.
Clem