If you are lucky, your new rad will come with plastic caps covering the atf in/outlet. When I replaced mine, I disconnected the bottom hose first. I quickly screwed one of the caps onto the rad outlet and bunged up the hose. Lost about an egg cup full. Capped top, removed rad and drained atf into an old measuring jug. Filled the new rad with same amount of clean atf, capped it and installed it a la Haynes.
An old mate (a plumber) told me this method of connecting up live is called the 'snatch' method. My understanding of US slang is limited and dated but I believe this may not be something you say over tea with the vicar
Oct '00 E46 330i. Feb '92 525i (departed)