Which came first, the Perlmonks or the CPAN::Forum question? heh. As the answer there states, DBD::Pg is not able to be accessed from multiple processes concurrently, so the suggestions to use a permanent table, or use Net::Server::Multiplex seem fair. You could also use some form of IPC to marshall access to the database so that it occurs only in the parent (which may defeat the purpose of using a forking server though, if your main point of blocking is writing to the database).
Also worth noting is that DBD::Pg supports asynchronous operations, so you could use asynchronous operations on a single DBD::Pg handle and use IO::Multiplex instead of PreFork if writing database records was the major blocker.
If you are just reading from the table in your children (writing does seem a little strange, since it is to a temporary table, which will die with your session), then you could read the whole table into a hashref/arrayref in the parent and have your children access it using Perl syntax instead of DBI.
Still, I think we would need more detail to provide a more helpful answer.