If your radiator is cold at the bottom there is just a chance its blocked at the bottom where any sludge can gather. Ive had the same problem myself this weekend on my CBR 1000 FL. I initially tried flush the the system with Wynns flushing fluid but that didn't work. So I started by undoing hoses and with the gundge that came out I began systematically cleaning each rubber hose ...pressure washing the engine waterways ....taking off and cleaning the water pump. And as we speak the radiator is off and having been steamed with the old wall paper steamer has started to give up the gundge which lay at the bottom. Once the rad matrix has been completely cleaned and you have a good flow re fit to the car fill with new coolant and run her again. If the rad is still cold at the bottom it's probable the matrix has had it in which case its time to get the wallet out. Good luck cheers

Graham

Waking up is a good start to the day !!