How deep is the ocean there ? NZ itself is evidence of underwater mountainous geography nearby.
Is it impossible that sun warmed air at 110 degrees could warm water 5 degrees at a depth of 60 feet ? Doubtful, imho. Common sense tells me no way in hell.
Speaking of hell, 1000 degree vents could do the job causing hot water to rise, especially if the vents were not at extreme depth.