In the Remote Terminal Client, under "Local resources" you can enable "Drives", so your local drive becomes available on the remote computer (so you can copy files between them). Alternatively you may want to try
UltraVNC as a terminal server and client. It's an improved RealVNC which features file transfer capabilities. Also it's able to work with DirectX video rendering modes or even overlays. It can use a WinVNC video driver for improved performance (optionally).