When cycling a hospital or quarantine tank I generally put the sponge filter in the main tank for a week, to get it nicely colonised with beneficial bacteria and transfer the sponge filter, plus some main tank water when I'm ready to use the hospital tank. Sometimes I put a stocking with matured gravel in suspended in the tank as well, near an air-stone, as I don't want to have gravel in the bottom of the tank. I don't specifically "cycle" the hospital tank as such.