No, you don't. Because the milk solids and water are removed from the butter what's left is pure fat and it is shelf stable when stored in an airtight container. Bacteria requires water to multiply and therefore won't grow in ghee, just like it doesn't grow in olive oil or other types of cooking oil and fat. You can safely leave ghee at room temperature for 6 months or more as long as it has been cooked and strained properly. If you see any solid particles in the ghee after straining, you will want to strain it again. If you aren't sure, you can always refrigerate it.