First off, you don't have a /tmp partition. The files stored in /tmp are in fact stored in the / partition.
I don't know off-hand why the files aren't being cleared out; I'd assume that it would be a problem with the program writing them.
If the directory is always called /tmp/logwatch.OJp30518 then you have the option of creating a symbolic link to another directory, like this:
Code:
cd /tmp/
rm -rf logwatch.OJp30518
mkdir /var/logwatch_temp
ln -s /var/logwatch_temp logwatch.OJp30518
This will cause any files written to /tmp/logwatch.OJp30518 to be written to /var/logwatch_temp instead.
You could use gnuparted to resize your / partition (you can find it on freshmeat.net). You also have the option of creating a partition of type tmpfs, which will be stored entirely in memory and hence cleared on each reboot (this will take up RAM, but not disk space). You'll find instructions on that if you search LQ for tmpfs.