The ship, which is carrying more than 1,000 people, lost power on Monday in the Indian Ocean after a fire in its generator room. It has no lights or air conditioning, so helicopters are flying in food and supplies to the stranded passengers and crew.
"The speed of the ship, despite the hot and humid climate, creates a slight breeze that helps make the situation more comfortable," a company statement said.
The incident comes just six weeks after the Costa Concordia hit a reef and capsized off Italy, killing 32 people. Both ships are operated by Costa Crociere SpA, which is owned by Florida-based Carnival Corp.
No one was injured in the fire, but the ship is currently in an area where Somali pirates are known to attack. It is being escorted by the Seychelles coast guard ship Andromache and an air force plane.
The Associated Press contributed to this story.