Doing some digging, and reading over what I've been able to find, it looks like several things need to be done. My reference on this is
http://www.microsoft.com/windowsxp/using/networking/expert/russel_05Feb.mspx which pretty much seems to describe the entire process.
Looking over the user guide for yor Linksys RT31P2, there are some changes that will need to be made to its setup, and to your HOME desktop machine.
The Linksys needs to be set up for port forwarding, for TCP port 3389. But, it needs an IP address of the HOME desktop. If the desktop machine is getting a dynamic address, it may or may not get the same address each time.
So, the desktop machine will need to be assigned a static address. The Linksys provides addresses in the 192.168.15.x range (where x is 100 to 149). The desktop needs an address outside that range, but within the range of 1 to 254. For the sake of presentation, I'll assume the desktop is assigned 192.168.15.80.
With the desktop given a fixed address, then you can login to the Linksys, and go to the "Applications and Gaming" tab. Here you will need to enter the details for the port forwarding:
application: some name - it's a label for your use - call it "remote desktop"
start and end: 3389 and 3389
protocol: TCP
IP Address: 192.168.15.80 , this is the LAN address of your desktop
Enable: yes, check the box
then "Save" to apply the changes. Linksys will now pass Internet traffic to your desktop on port 3389.
On your desktop, since you can already use remote desktop on your LAN, I would presume the CFP rules are already in place and working. You should have at least this rule present in your firewall Global Rules:
allow TCP in from any to zone[MyLAN] where srcport is any and destport is 3389
At this point, you should be able to access your desktop machine from the Internet. Which raises a boatload of security concerns. I'm a LAN/email admin on dayjob. From site firewall logs, I know that port 3389 is very heavily scanned. I would presume the scans to be folks looking for open machines. You're opening up a machine, so I can almost guarantee that your desktop machine will be attacked.
At the very least, have a very very good password on the Windows login. If the desktop is an XP Pro machine, I'd strongly suggest seting up a PPTP VPN so you have an encrypted connection and a second layer of passwords.
Since the desktop machine is running CFP v3, I also strongly suggest you make the full use you can of Defense+ to harden your machine.
This should get you going using the remote desktop. If, in your traveling, you use wireless hotspots, be aware that remote desktop isn't, so far as I know, an encrypted connection, and hotspots are usually very easy to sniff.