Here is a simple thermostat circuit that can be used to control a relay and supply power to a small space heater through the relay contacts. The relay contacts should be rated above the current requirements for the heater.
Temperature changes are detected by a (1.7K @ 70F) thermistor placed in series with a 5K potentiometer which produces about 50 millivolts per degree F at the input of the LM339 voltage comparator. The two 1K resistors connected to pin 7 set the reference voltage at half the supply voltage and the hysteresis range to about 3 degrees or 150 millivolts. The hysteresis range (temperature range where the relay engages and disengages) can be adjusted with the 10K resistor between pins 1 and 7. A higher value will narrow the range.
In operation, the series resistor is adjusted so that the relay just toggles off at the desired temperature. A three degree drop in temperature should cause the relay to toggle back on and remain on until the temperature again rises to the preset level. The relay action can be reversed so it toggles off at the lower end of the range by reversing the locations of the 5K potentiometer and thermistor. The 5.1 volt zener diode regulates the circuit voltage so that small changes in the 12 volt supply will not effect operation. The voltage across the thermistor should be half the supply or about 2.6 volts when the temperature is within the 3 degree range set by the potentiometer. Most any thermistor can be used, but the resistance should be above 1K ohm at the temperature of interest. The series resistor selected should be about twice the resistance of the thermistor so the adjustment ends up near the center of the control.