Temata, 52, had recently returned to New Zealand for medical treatment, Tagata Pasifika reported.
"On behalf of the government and the Foreign Affairs Ministry, we extend our deepest sympathy to Tessa's family, friends and colleagues," Mr Peters said.
"A respected diplomat with more than 25 years of experience in trade, development and legal matters, Tessa made a particularly strong contribution to deepening New Zealand relationships with Pacific Island countries."
Temata was New Zealand's first High Commissioner of Cook Islands descent to serve in the Cook Islands, and also the first woman New Zealand High Commissioner of Pacific ancestry to be posted to the Pacific. Temata's family lives in Samoa and the Cook Islands.
Since joining the Foreign Ministry in 1992, she had postings in Indonesia, Papua New Guinea, Kiribati, Niue and Cook Islands, Tagata Pasifika reported.
Peters said this was a difficult time for Temata's colleagues, particularly those at the High Commission in Rarotonga, who all knew her as courageous and inspirational.
"Ms Temata served her country with great distinction," Peters said.
"The Pacific is the part of the world where New Zealand can and does make the most difference. It is therefore to Ms Temata's great credit that she spent so much of her career serving right across the Pacific.
"She demonstrated how much of a difference expertise, warmth, hard work and cultural competence can make to New Zealand's Pacific diplomacy. She will be hugely missed," Peters said.