Nut oils can rapidly become rancid if stored at higher temps and also if it is exposed to air for prolonged periods.
The critical temp seems to be about 80-85° F. - 26-29+°C.
I smell and taste any oil before using it in a recipe. It is instantly clear that the flavor is off, as soon as you taste it.
I don't keep my oils in the fridge but I have a "cool room" where I store them and I make sure the cap is tightly fastened and store them in plastic buckets -up-side down. This lessens the amount of oxygen (the great destroyer) that can get to the oil.
I store salad dressings, mustards and other condiments this way also - the reason I use containers to hold all these smallish bottles and jars in the fridge.
(It also takes less time to search for one item and makes it much easier to clean the fridge.)