Here are the two hoses which connect to those lines on the top rear of the radiator:
The big one is the main line connecting to the thermostat on the back (left) side of the head assembly. But what does this little one do? The other end is connected to the fuel injector manifold back (up) here:
Then comes out the back side and connects to the little nipple on the side of the thermostat housing which can be seen in this photo.
No, don't look where I'm pointing (that's the clutch cable). Look above my knuckle near the middle of the photo and you can see the tiny shiny receiver line. This is very cool....er hot, I guess. We have a "heated" fuel injection manifold! So, I don't think we'll ever have "icing" problems clogging up our injector ports. Oh....how I remember the days of fighting Carb Icing. They are all gone now!
And, here's one more TRICK for dummies
There's getting to be so many wire connectors and hoses to be disconnected, that I decided I better start labeling them....for good measure. A roll of masking tape & a permanent marker make a great companion in a project like this. Your camera too! Take lots of "before" pics as you disassemble. Then, you have something to reference upon reassembly, if necessary. You never know how long you'll bike will remain in pieces when you start a big project like this. Could be a week or two later, before you put it all back together. So, steps like this can come in handy. Sometimes I find myself saying, "now how was this routed &/or connected before I took it off?" Man, those photos can sure come in handy!