Technical Question: Unifying overlapping CSV files

I'm sure someone out there has dealt with this before, so here goes. We have a process that outputs, once every half hour, a CSV file of the last X lines from a given log. The activity recorded in this log has peaks and valleys, so the last X lines might only cover the last hour's activity, at busy times, or might cover the last six hours, when things are quiet. The end result is that the output CSV files overlap unpredictably.

Is there a tool, script, process, or anything of that sort - anything in Windows, or shell scripts in Unix - that can unify a bunch of these CSVs into one CSV file? I can do it manually in Excel, but it's a pain.

I can probably work out something in the shell script line with diff and head, but it would be nice if someone has already got one knocking around.