Lee Douglas Perry has been named as the man whose body was found in the water near Ostend on Waiheke Island on last Wednesday 15 November.
Police said the 48-year-old from South Auckland had travelled to Waiheke earlier in the week for work.
Detective Senior Sergeant Chris Allan said police were "continuing to treat the death as unexplained", as enquiries are made.
"Police are wanting to establish the circumstances of the death and the discovery of a burnt-out vehicle, which we can now confirm belonged to Mr Perry, and was located around 14 kilometres away from his body.
"We are appealing to the public for information regarding the movements of Mr Perry from Monday 13 November, in particular on or near Wharf Road, Ostend Road, and Man O War Bay Road, on Waiheke Island.
"Additionally, anyone with information on Mr Perry's vehicle, a white Mazda Demio, registration HLZ228, while on Waiheke Island, is asked to get in touch."
The car was found crashed and burnt out on Man O War Bay Road on Wednesday morning, Allan said.
"Police would like to understand how it got there."
It was previously seen on Wharf Road on Tuesday.
Anyone with information about the case is asked to contact police.