When you do the flush you don't have to remove the thermo. What I do, is that with the engine cold, remove the top hose from the radiator, and aim it downward into a bucket (It's illegal to dispose of coolant on the ground I think) and then start the car, and feed a hose right into the radiator once the car hits temp and opens the thermostat. It'll keep keep water running through the system. (use a radiator flush solution sold in stores. You drain radiator, fill with solution and water, let car run for about 10 minutes warm) then at that point just do the flush with a hose. When you see that the water comming out of the hose is comming out clean fresh water, turn off car, turn off hose, drain radiator, connect hose, and fill with the coolant. There's still water in the system. I don't know how much it will take, but if you need more, then add water to top off. put 50/50 in the resevoir.

PS. Don't forget to open bleed when doing final fill, have your heater on high when the car is running, and to check your levels after the frist drive.