The Association of Mineworkers and Construction Union (Amcu) and workers will apply to regain access to the mine's hostel, after they were locked out on January 3.
On Tuesday, Judge Ndawoyakhe Tshabalala asked what the urgency of the application was, since Harmony Gold had offered to transport miners home.
Ivan Miltz, for the miners, argued that their livelihoods were affected and many of them were "put up in a tent".
The court heard that the replying affidavit was handed in late and Tshabalala had not had time to study it.
On January 3, miners were told the mine had been shut down until further notice in order to review operations after several illegal strikes. Miners were denied access to the hostel and many slept outside the gates.
In December, 1 700 workers at the Kusasalethu mine had a sit-in demanding that their fellow employees, who had been suspended, be reinstated. Amcu and the miners had representatives in court on Tuesday.
The application is scheduled to be heard at 10am on Wednesday. – Sapa