You can keep them out of the refrigerator for short periods of time, but for long term storage, they really need to be kept refrigerated.
Those implants are designed so that the binding material breaks down when heated to body temperature thus releasing the hormones to be absorbed by the blood stream. The lower the storage temperature of the implant (without freezing), the more stable the pellet, the more available hormone once its used. If they are stored at a higher temperature the pellets will break down, and you will lose potency. I've seen them literally melt to a glob when stored in the back of a vet truck through the summer when the refrigerator broke.
