Not too sure why your bike starts with a code 4, could be a stored fault code? Not too familiar with the R/X diagnostic display. Sorry.
However! If it were me; I'd start with the temperature light coming on prematurely and when the engine is cold. Check the sensor connector is firmly clicked home and all the wiring for shorting to earth, physical breaks and points of high resistance (trapped wires, worn through insulation, corroded connectors, melting connectors). Also check the multiplug at the ECU end. The temperature sensor wires are blue/black and green/red.
Water damaged/corroded connectors and wiring rubbing through are well documented faults on R/X (and Z), particularly where they eye doesn’t see, like under the tank. Get your tank off and have a good butchers at the wiring before you try anything that’s going to cost you money!