For the white smoke to clear once everthing get warmed up is the normal thing to happen. Takes a bit longer to clear in cold and damp conditions. Running the engine with no load also takes longer to clear. I wouldn't be too hasty in changing the head gasket unless you are absolutly sure that's the problem. It probably isn't that.
The cap on the thermostat housing is spring loaded for the bottom seal, with another seal under the top of the cap. This allows the water, when it becomes pressurized due to expansion as it heats up, to escape through a small pipe to the expansion bottle. On cooling the water gets sucked back through a small valve in the cap. That's the silver disk at the bottom of the cap which you can see on your photo. There isn't to my knowledge a cap on the radiator on the FZS600.
Lets hope it's just a split pipe. Good luck.
The cap on the thermostat housing is spring loaded for the bottom seal, with another seal under the top of the cap. This allows the water, when it becomes pressurized due to expansion as it heats up, to escape through a small pipe to the expansion bottle. On cooling the water gets sucked back through a small valve in the cap. That's the silver disk at the bottom of the cap which you can see on your photo. There isn't to my knowledge a cap on the radiator on the FZS600.
Lets hope it's just a split pipe. Good luck.