Let's first fully realise how small the area below 400 m altitude is :
http://www.lordhoweisland.info/skeoch9_jpg_view.htm
... and that the temperature difference between these two worlds is not only due to altitude but also to the extreme sunshine difference, like the cover
photo for this thread also perfectly illustrated
http://www.lordhoweisland.info/skeoch8_jpg_view.htm
palms in habitat, in altitude
http://www.lordhoweisland.info/skeoch13_jpg_view.htm
planted palms - even as adult and under the shadow of (introduced) Norfolk Island Pine it has burnt fronds
http://www.lordhoweisland.info/skeoch3_jpg_view.htm
no palms growing spontaneously in this islet
http://www.lordhoweisland.info/skeoch2_jpg_view.htm
Howea forsteriana in lowlands were planted, after being grown in nurseries in the shade.
It's the only palm that is planted simply because it is also the only palm whose seeds are exported.
http://www.lordhoweisland.info/environ/kentia.html
Anyway, for the palms example, I made the mistake of mentioning only temperatures in the introductory article. I should have stressed the cloud cover factor, which during an ice age would have been also much different.