I'm not getting a Temp alarm, but it seems like the bike is overheating or theres issues with the coolant circulation.
You definitely have issues with cooling but circulation is only one of the factors that could be at play.
As frankenduck implies, radiator caps and gasket can wear out, but regardless of whether the radiator cap is faulty, the temperature sensing relay is not triggering the temperature warning lamp in the instrument cluster as it should when the engine overheats. We know
that because coolant boiled over without warning. Failure to light the warning lamp could be caused by a faulty coolant temperature sensor located behind the radiator.
The sensor has two wires; one sends a signal to the fuel injection control unit to adjust mixture according to engine heat. The other wire sends a signal to the temperature sensing relay that responds to heat by triggering the fan. If the engine continues to heat, the relay then triggers the warning light in the cluster. There could be breaks in the continuity of those wires, or the coolant sensor itself could be sending faulty signals. While you
can ride after you install the new cap and gasket, the engine will
still overheat if the fan isn't working. That will cause coolant boil-over if you're trapped in jammed traffic on a hot day. You might like a warning before that happens so you can move to the shoulder and shut down your engine for a minute or two. I suggest this malfunction be remedied soon.
The fan could be seized. It can be checked for operation. Use a dowel for spinning the blades to determine if they are seized. If they spin, terminals in the temperature sensing relay can be jumped to determine if the fan
motor works.