I am curious about that too so I went searching. This is the best explanation I found regarding hot springs and extinct volcanoes.http://www.teara.govt.nz/en/hot-springs-mud-pools-and-geysers/1How do geothermal systems work?
Geothermal water starts life as rainwater, which seeps down though cracks in the rock towards a heat source deep within the earth. Hot water is less dense than cold water, so it rises and emerges at the earth’s surface, sometimes as steam or mixed with steam. The hot water reacts with the rock it comes into contact with, and becomes enriched with dissolved minerals.
New Zealand’s geothermal systems
Scientists divide New Zealand’s geothermal systems into three main groups:
•Large, intense systems associated with young volcanoes
•Cooler systems associated with older or extinct volcanoes
•Isolated warm springs associated with faultlines.
The Taupō volcanic zone
The major geothermal fields in the Taupō region give rise to the spectacular geysers, boiling springs, mud pools and fumaroles (steam or gas vents) throughout the region. These features are closely associated with active volcanoes. In volcanic zones such as Taupō the ground is heated by magma (molten rock) close to the surface.
Because of this intense heat source, water temperatures in the deeper parts of a geothermal system may be greater than 300ºC. The waters are under great pressure, so can become superheated well above their normal boiling temperature (100ºC at sea level).
Outside the Taupō region, the only other high-temperature geothermal system is at Ngāwhā, in Northland, which has been volcanically active in the last few thousand years.
Cooler systems in volcanic zones
Numerous other hot springs are associated with remnants of volcanic activity, particularly in Northland, Coromandel, the Hauraki Plains and the Bay of Plenty. Heat sources for these fields are diffuse rather than intense, producing fluid temperatures of less than 100ºC.
These smaller systems are confined to the North Island. Banks Peninsula and Otago Peninsula in the South Island are ancient volcanoes, but there is no longer any volcanic heat flow underneath them.
Springs associated with faultlines
Warm springs (less than 70ºC) are found in non-volcanic areas of New Zealand. Faults – deep fractures in the rock – provide channels for warm water to rise rapidly from depths where it has been heated. Striking examples are the hot springs aligned along the Hope Fault, in North Canterbury, and the Alpine Fault, in the Southern Alps. At Hanmer, on the Alpine Fault, a range of thermal pools attract thousands every year.
the diffuse heat source explains why the hot springs around Auckland (Waiwera, Parakai and Miranda) are a long way from the volcanoes