Are you talking about this software: http://www.cis.uni-muenchen.de/~schmid/tools/TreeTagger/ ? If so, a quick look at that page seems to show that you can give it input via STDIN. A module such as IPC::Run, IPC::Run3, or Capture::Tiny may be able to help you. However make sure to read their documentation, as they might not actually be more efficient than the way you are doing it, for example, IPC::Run3 uses temporary files internally in several cases. It's just easier to use than doing all the temp file stuff yourself.

Have you tried out the Perl interface Lingua::TreeTagger? It looks like the install may be a bit tricky, but if you install its prerequisites manually you may have success.