Temp files are cleaned in Ubuntu by systemd-tmpfiles and the related service /lib/systemd/system/systemd-tmpfiles-clean.service, and the configuration for said files can be configured inside /etc/tmpfiles.d/*.conf (also see this answer).
To include the directory you describe, create a config file:
sudo touch /etc/tmpfiles.d/scratch-tmp.conf
And then include this content in it:
# Type Path Mode User Group Age Argument
e /scratch/tmp - - - 20m
The e type defines that this is a "marked" directory that already exists, but should be cleaned. An age setting of 20m will clean all files more than 20 minutes old (see explanation below).
If the type is d, the directory will be created if it doesn't exist, and cleaned up on reboot and each day.
Be aware that the timer triggering the service (found at /lib/systemd/system/systemd-tmpfiles-clean.timer) is set to run 15 minutes after boot, so you won't see the actual effects at reboot until after 15 minutes uptime.
Please see the manpage for tmpfiles.d for more information.