25-year-old Albanian, Oljan Tusku and Turkish-born Murat Eksi climbed onto a roof of the centre near Port Augusta Wednesday in protest at their continued detention.
They say they'll continue their protest until they're allowed to stay in Australia.
An immigration spokeswoman says the men have been visited by a mental health team and have been given blankets, hot coffee and sunscreen.
Mr Tusku says he's been in immigration detention for nearly two years despite being married to an Australian citizen.