So, suppose there exists an island (roughly the same size as Hawaii's big island) which is located well in the arcticArctic (or antarcticAntarctic) circleCircle, but magically has a tropical rainforest climate (warm temperatures, lots of rain, and bright sunlight even when the rest of the hemisphere is experiencing polar night.)
The climate is maintained by magical means, and has existed this way since before the evolution of modern humans, at the very least. It may have existed this way for much longer. At least part of the magic works by maintaining an artificial sun over the island (much smaller than the real one, located within the upper atmosphere. The artificial sun does not provide significant light or heat outside of the island's immediate vicinity.)
This artificial sun shines only on the island and the water within an arbitrary distance. Let's say that this distance is five miles, just for the sake of argument.
What climacticclimatic effects would this have on the island (outside of the artificial tropical climate), the local region, and the world as a whole? I am looking for weather, climate, and biological effects particularly, but any other notable effects I would like to hear.