Pretty long. Eventually I went to Rabao to check the Weather Reporter, but he kept saying Dust storms for the next three days. I just got lucky and a Heat Wave appeared for a few seconds, and I grabbed it. I waited while doing other things IRL after you left for about three hours, went to bed, woke up, went to work, came back and waited for two hours or so and that's when it popped up.
Do you know anything about the avatar battles? Mini-Terrestial battles?