Amaryllises are perishable live plants and will start to grow if you leave them at room temperature.
Storing the bulbs in a dark room or place anywhere at consistently 41 to 47 degrees might slow down development. Do not place the bulbs in the refrigerator. It is also important not to store the bulbs near ripening fruit. Ethylene gas given off by the ripening fruit can damage the bulbs.
Be careful not to expose the bulbs to freezing conditions!