If /var/tmp is a tmpfs its content is deleted on reboot and logcheck complains about missing file or directory:
/etc/logcheck/logcheck.sh: line 189: /var/tmp/logcheck/check.9861: No such file or directory
If logcheck expects logcheck/check.* to be persistent it should not use /var/tmp which is for temporary files. Otherwise it should re-create the missing file or directory.
it seems that we are the last distribution still supplying this package. Cannot it be replaced by other tools?
Regarding the dir... we could change it I think, but I am not sure about the purpose of that "temporal" directory. How is it really using it? If the files there need to be persistent... it doesn't look like a "temporal" dir to me and, then, its location should be different (like /var/lib...)