No, acrylic paints should not be stored outside as environmental factors can affect the paint's properties. If you wish to store acrylic paint for a long time, select a well-ventilated area where the moisture can't get into the container. Also, the paint container must be airtight.  As for temperature, it shouldn't be too hot or too cold. The optimal temperature for storing acrylic paint is 65°F to 75°F.