The volcanic and geothermal activity of New Zealand coincides with the Havre Trough, where the Pacific Plate is subducted under Zealandia, as explained here: https://en.wikipedia.org/wiki/Geology_of_New_Zealand
According to my analysis, main division line of the convection rolls system passes New Zealand and affects the trough, explaining anomalies in the area.

The width of the area fits above one convection roll, just like the Icelandic volcanic zones. Therefore, to understand the geothermal activity of New Zealand more thoroughly, the mantle convection currents should be taken into account.