Sure. Hiawatha has a 'working directory'. In this directory, the unix sockets for FastCGI are stored, a directory with temporary data for the Hiawatha Monitor and a directory for file uploads (PUT requests). The default location of this directory can be found in the manual (is installation dependent). For Debian, it's /var/lib/hiawatha. You can change this to /tmp/hiawatha via the WorkDirectory setting.
WorkDirectory = /tmp/hiawatha