What type of space heater are you using. Oil filled seem to work the best ad I think are some of the safer ones out there. I would avoid any heater with open coils/heating elements.
Also when you are running the heater make sure it is the center of the room and around 3ft from anything. It would also be a good idea to get a thermostat for it. Be carefully which therm you get cause some say not to use with an oil filled heater.
Is there any kind of fan in the room for air circulation. It is preferable to have a consist room temp rather than hotter and cooler spots.