I think it depends on the company making it. Walnut oil has become popular because it has Omega 3s in it -- or it CAN have Omega 3s in it.
Usually, and unrefined oil is either cold-pressed or expeller-pressed. Cold-pressed means the nuts or seeds are squeezed to get the oil out, but the temperature doesn't go above 160 degrees Fahrenheit. Expeller-pressed does the same thing but squeezes even harder, and temperatures can go up to 200 degrees Fahrenheit. The oil is then usually (but not always) filtered to remove any pieces. Unrefined oil usually retains its full flavor and color and many of its nutrients. But it is delicate. You HAVE to store it in the refrigerator. The exception to that rule would be an unrefined saturated oil, like coconut or palm. They don't have to be stored in the fridge. Heat over 180 degrees Fahrenheit can damage essential fatty acids and create free radicals in many unrefined oils (saturated oils being the exception again). Temperatures above 320 degrees Fahrenheit can make unsaturated fatty acids form trans-fatty acids.
A refined oil starts out being squeezed and pressed but then solvents are added to get even more oil out of the plant material. Hexane is a comment solvent used. After the solvent extracts all the oil, it is then heated to about 300 degrees Fahrenheit to burn off the hexane (it's kind of like
gasoline). Often the solvents and additional heat create nasty flavors and sometimes make the oil rancid. The oil then gets degummed, bleached, and deodorized with temperatures over 460 degrees Fahrenheit. The result is an odorless, almost tasteless oil that is stripped of its phospholipids and can withstand much higher heat than an unrefined oil.
I'm being overly basic though. A lot depends on the oil -- whether it is polyunsaturated, monounsaturated, or saturated. Many
books have been written discussing this.
Anyhow, you asked about walnut oil. I would use cold-pressed only and store it in the fridge. I would buy a small bottle because eventually it will go rancid even in the fridge. I wouldn't heat this oil very much, if at all. Walnut oil is delicious in salads or very lightly heated in different dishes, often added at the end.
I hope this helps.