Rinse the sunflower seeds in a colander under cold water. Pick through them and remove any stones or debris that you find. Spread the rinsed seeds out into a single layer on paper towels so they dry completely.
Dump the clean oilseeds into a food processor. Pulse the blades to break up the seeds and hulls until the volume of plant matter has reduced by about two-thirds.
Pour the chopped seeds into an oven-safe dish. Slide the dish into a preheated 300 degree Fahrenheit oven. Turn the material in the dish with a spoon every five minutes to heat it evenly.
Insert the tip of the probe thermometer into the chopped seeds after they have been heating for 20 minutes. Remove the dish when the internal temperature has reached 170 degrees Fahrenheit.
Load the heated oilseed mash into the home oil press or seed oil extractor. Press the oilseeds through the machine with the plunger until all the material has been pressed. Use the collected sunflower oil immediately or store it for up to two weeks in an air-tight container in the refrigerator.