The operation to defrost the 10-metre (34 feet) long, half-tonne squid began on Monday afternoon in Wellington following a postponement of 24 hours.
The animal is now sitting in a bath of salt water. Once it is thawed, scientists will begin to dissect it.
Very little is known about colossal squid, which appear to live largely in the cold Antarctic waters and can grow up to 15 metres (50 feet) long.
“They’re incredibly rare – this is probably one of maybe six specimens ever brought up,” said Carol Diebel, director of natural environment at the Museum of New Zealand Te Papa centre.
“It’s certainly the one that we’re being really careful about, completely intact and in really fantastic condition.”
The Mesonychoteuthis hamiltoni specimen was caught in February 2007 in the Ross Sea. – bbc