The true statements are
"Its temperature will rise until reaching 0°C."
And
"Its temperature will remain at 0°C until all the ice melts."
So, basically once the ice has reached 0°C we can conclude that the ice has probably fully melted. However the temperature has to stay there if we want the ice to melt.
We must remember that the melting point of ice is 0°C, and that Ice is completely melted at approximately 0°C so we must have those two statements true