I aim to connect my fedora host running some matlab code and check its status at present. Is is it possible to connect to the host from Windows 7 machine and see the curret desktop environment as remote desktop? If it is, how could I do it? I know Putty works fine for ssh but does it for remote desktop too ?
It's feasible - you'll need an Xserver on Windows ( Xming, for instance) to handle the Xserver display. You'll also need to configure putty to enable X11 forwarding.
This post explains how you can piece the two parts then. To summarize: