Oils do go rancid. Heat, light and air make them go rancid. Nut oils are particularly sensitive to going rancid.
The absolute best place to store oils is a wine cooler and if you had a rather large collection of expensive oils and wines, I would highly recommend one for you.
However, if that isn't an option, I would store all my nut oils and high cost oils in the refrigerator. They will clot up but will loosen up after a few minutes on the counter.
You could keep a small jar well sealed in the pantry well away from the stove or oven and keep the larger container in the refrigerator.
Sesame oil is another oil that is very sensitive to going rancid.
Try not to store your oils in one of those bottles with the open pouring nipple. At the very least get one with the snap closed cap.