Just to confirm, it IS an FZ6, you have it noted as a :" fx6r " CORRECT???
How many miles on the bike and when was the coolant last changed?
Where I'm going is in the the last picture posted above (by FinalImpact) , if those coolant hoses (IAC) are clogged
The engine will think its ALWAYS COLD and keep the engine running in the "enriched mode" .
I would be specifically inspecting those two ports in the IAC, (hook up two hoses and see if water flows easily thru them)
plus visual. Why the hoses are off, (and its going to make a mess if functioning correctly), start the bike
and see IF YOU HAVE COOLANT FLOW going into it, and perhaps blowing into the "exit" should that be clogged.
Of course, fluid should flow easily thru the unit...
There is NO adjustment to speak of for the "COLD MODE".
The air adjusting screws- for normal syncing, or by-passing and adjusting the CO settings, etc, may affect running cold.
**If the 4 air screws (on the same unit) have been adjusted, the "starting point" is 3/4 a turn out from lightly seated..**