Personally, I would look into a radiating heater first. I'm always wary of space heaters, I've seen too many cases in recent years of folks burning down their houses. I'm sure this is depending on the model of heater, but ...
If you must get a space heater, look into an oscillating ceramic tower heater. Most of them have a digital thermostat on them and can hold a temperature range. If placed in a proper enclosed (but vented) place, you can hold a solid temperature range without the heater turning on nearly as much.