Modify the existing duct system to include vents for the basement. This will require the help of a professional HVAC contractor. By diverting some of the home's heat to the basement, the space can be kept at a relatively constant temperature.
Install a wood or pellet stove in the basement and vent it out through an exterior wall. If you are interested in alternative heating, either one of these options will work for a basement. Keep in mind that you will need to check the pellet or wood levels regularly to keep the heat at a regular temperature in the room. Too much wood will make it unbearably hot, and if the stove goes out, then the room will return to icy temperatures.
Utilize infrared heaters in the space. These heaters warm the objects in the room, not the air. They can be set with a thermostat to help maintain a certain temperature in a space. Most are rated for use in spaces that are less than 1,200 square feet for larger models, and less than 500 square feet for smaller models. If run continuously, this type of heater will keep the space warm, even if the ambient temperature feels slightly lower since there is no blower on the heater. This type of heater is much more efficient and safer to run than a space heater.