This week's book giveaway is in the OCAJP 8 forum. We're giving away four copies of OCA Java SE 8 Programmer I Study Guide and have Edward Finegan & Robert Liguori on-line! See this thread for details.
You could write 2 programs, one running on either machine. The one on the *nix box sends a signal over the network when run, this one you schedule. The one on the NT box listens for this signal and if it receives it starts your Windows application.