Cooling system was a bit of mystery. I heard a strange noise coming out from radiator fan. As the radiator was finally removed I found the source of that clang.
I searched through the Kawi forums and find out that Akrapovic exhaust pipes installed on my bike could be closer to the cooling fan than OEM and that could be the reason for melted wing. There are aluminium made radiator fans available on ebay. Another idea found on the web was to install the short-cut switch. But wait... start the fun by a switch? Let's try basic methods first. Radiator was flushed to eliminate the built up of rust and sludge from inside.
I've ordered a second-hand fan (comes with guarantee for one year :-)
Cooling sensors checked... The one installed on the radiator is responsible for starting the fan. Mentioned short-cut switch can be connected here. In the end it turns out that is unnecessary and nicely done switch remain for different purpose i.e. folding license plate ;-)
Thermostat checked... Temperature sensor installed on the thermostat housing is responsible for gauge indication. There is a simple way described in service manual, to check it with use of jumper wire.
Then it comes to the cooling system filter installed on the side of the engine... It looks scary to me. I was wondering how long she rides with that glued something.
And at last reservoir tank. Another part with a pile of epoxy on it.
New one comes together with radiator fan.
I put it back together, fill up with fresh coolant and since then it runs perfectly. Temperature sensors indicates correctly, fan starts when it should. In a word - problem solved.