Optional: execute the following once (see http://hacks.oreilly.com/pub/h/66 for
details), to avoid typing in the password.

   1  
   2  set LINUX_HOST=mylinuxhost
   3  ssh-keygen -t rsa
   4  ssh %USERNAME%@%LINUX_HOST% "mkdir .ssh; chmod 0700 .ssh"
   5  bash -c 'scp ~/.ssh/id_rsa.pub %LINUX_HOST%:.ssh/authorized_keys2'

Now, if you save the following as a BATCH file, you can just click it
to connect to fullscreen Linux:

   1  
   2  set LINUX_HOST=mylinuxhost
   3  start /min xinit 
   4  xhost +%LINUX_HOST%
   5  ssh %LINUX_HOST% "declare -x DISPLAY=%COMPUTERNAME%:0; echo $DISPLAY;gnome-session"'

NOTES:
1.
Sometimes xhost + does not execute in time. O well. Just close
all windows that got opened and try again.

2.
If you didn't do the step one (ssh keys), you will be prompted
to enter the linux password; this increases the chances of the above
error.

3.
The single terminal window appearing in the Linux desktop is in fact
a window from your PC.