S4Rt Overheating?

[ChchS4]

My S4Rt fell-over (long, unhappy story ) and a small coolant drip developed from the drain plug on the water pump cover where it hit the concrete. I replaced the plug and copper washer and following workshop manual instructions, refilled the cooling system through the overflow tank. The drip is gone.  However, now the bike is reaching "Hi" (120C) during a ride and even while sitting at idle in the garage. The fans are coming on at about 105C.  I topped up the coolant through the overflow tank and much of the top up was spit out through the overflow tube.

Any suggestions?  Is it possible that the water pump is not working?  I notice that when the fans come on, the breeze coming off them is cool rather than hot but the two hoses going into the radiator are hot. However, the side of the radiator where the cap is, is relatively cool, when in fact I would think that it should be hot given that the hot coolant flows across the top of the radiator.

Any suggestions or advice very much welcome.

[Speeddog]

~~~SNIP~~~  
following workshop manual instructions, refilled the cooling system through the overflow tank.
~~~SNIP~~~

WTF?
<EDIT>
Checked, and the manual does indeed say to do it that way. 
Service Manual Proofreading Department must have been on a 4:20 break just prior. 

Take the radiator cap off (engine cool/cold) and fill it there.

It fills a bit slowly, so you've got to fill/wait about 10 times.

In the driveway or shop, run the engine up to 105C for a couple minutes.

Shut off, allow to cool, and refill the radiator again.

[ChchS4]

Bingo!  Thank you very much for the excellent advice. I hope that somebody back at Ducati notices this glaring error in their instructions on how to change the coolant on a S4Rt.  Many thanks again.