The fan doesn't cut in till the coolant temperature in the cylinder head reaches 102C, which is pretty hot (it cuts out again when the temperature falls to 95C).
I have a coolant temperature gauge fitted to mine (sender in the top hose), mainly because I don't trust warning lights (they only come on when it's too late!) Anyhow, it gives a good indication of what's going on.
I've attached a PDF of some temperature readings (against elapsed time at idle) which I recorded using the Yamaha diagnostic tool and my temperature gauge. Might be useful?
There's probably nothing wrong, just paranoia setting in as a result of your radiator cap issue!
If you're really concerned that the temperature warning light and fan are not being triggered by the ECU (feed off the same sender) then you could drain the coolant, remove the sender and test its resistance as the temperature increases whilst immersed in a pan of water on the stove (as per workshop manual)...
You could also get yourself a diagnostic tool. TBH, it's been well worth the outlay over the years I've had one.