I can think of two options, offhand:
1) Since you're already going to be storing some session
state (mapping the cookie to the temp table's name, if
nothing else), just add the last search terms to the retained
state.
2) Instead of saving the search terms with the session info,
you could also store it with the temp table (maybe even using
the search terms as part of the table name, with appropriate
precautions).
#1 is more straightforward, #2 allows you to reuse the
search results for anyone else who does that same search (such
as all the monks looking for SMITH JOHN right now). Either
way, though, you probably want to maintain this on the server
side instead of relying on the client to tell you which
set of saved search results to use, since the client can lie
to you quite easily.