It has to be kept warm. I've kept them in a moderate greenhouse..and it might have had some root rot at days of 65f and nights in the 50's..plus the short days. When the temps were moved up to 80f and 68f at night..it grew all year-and fast! Same greenhouse..only the temps varied.
So,its a $$$ decision on how much to spend to keep to near tropical temps.

I prefer forced air ceramic heaters versus radiant ones because I like how they heat up faster and distribute the heat better. Of course you could accomplish the same thing with a fan that comes on when the radiant heater is on.

i use a small 1500 watt ceramic heater that oscillates and it kept my 8'w x 6'd x 7'h lean to at 65 at night if I wanted to. Even when we had a week of nights in the teens it still did fine.

stan is right it mostly depends on how much money you want to spend on utility costs.

How big of an area do you have to heat?

Also,remember,the more insulated it is the less heat needed/provided.

Im not sure how much heat you would really need to provide. Daytime temperatures are pretty mild by you in the winter, its just night temperatures you need to watch out for. One thing thats very important is humidity! Im sure they would be browned to a crisp if they get too warm without getting some nice moisture. But if its cold and they are getting moisture, it will easily rot. Coconut palms are probably one of the least finicky palms you can grow in the tropics, but once you take them out of the tropics, they suddenly become very fragile, especially in the winter months.

-Alex

Thanks everyone for the reply :)

I dont want to spend too much, but I doubt I will need to. The green house is very small, I believe its about the same size as mksmths'. The winters here are mild. Averages are 50f's/40f's for high and lows. However, its mostly cloudy/rainy.We do get frost, but its rare.

- US_Marine