Hello all. I too have this problem on my 2004 R1 here in Oz.
Last year I had a coolant leak which progressed to a stage that it come out as fast as I could put it in. The bike would idle extremely high a few times just before I stopped riding it, which I thought had something to do with the low coolant level causing a sensor to adjust the idle abnormally.
I stripped the bike down, the o-rings in the water pump were bad, so I ordered parts from my local bike shop (around $600 for the pump and seals, to come from Japan). I just finished putting the bike back together after waiting 7 weeks for the parts.
It fired up alright, but once it warms up to the temperature where the idle should slow down, it slowly rises instead, thus causing the temp to rise quickly also. If I give it some throttle input the revs won't drop normally, because of the high idle.
Does anyone know what might cause this, a sensor, a bad ignition computer, the thermostat (which tests ok). I unplugged the PC3 but that didn't help. I guess I could get the local yam shop to swap a few sensors to fault find, but I'd rather check if someone else has had this problem and knows what caused it.