Colder temps slow all forms of chemical degradation. Oxidation, photolysis, and thermal are the primary ones for AAS oils, and cold slows all these aging processes significantly.
I would store it in the fridge. It'll last significantly longer. Or even freezer TBH if we're talking more than a few years. You'll have to reheat to recover from crashing either way, but that's harmless.
The only caveat about freezing would be to keep sealed in another container. If the rubber stopper shrinks to the point of losing the seal (it shouldn't but might if low quality), by letting it rise to room temperature in a sealed bag no risk of moisture condensation entering the vial from a compromised stopper.
The oil, BA, BB, and active ingredient are all undamaged in cold or freezing temps.