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Another old trick is loosen the joints unhook them from the brackets, lay the heads on the floor and tighten the joints back up. You have all the time in the world then to strip, line and paint the wall, but as Konastab01 says, a professional would be thinking how little they want to have to pay for new carpets or spend time cleaning up a spill.
It's worth learning to drain and refill the system of the house you live in.
The chap who painted our place was a whizz with this - took all the rads off the walls to paint behind them.