A look at this GEFS graph its showing a slight improvement from around the 17th onwards. The top part of the graph is the temperature at 5,000 feet and the bottom of the graph is rainfall.
So it shows a dip in temperature from the 17th to the 20th June then a sharp rise in temperature will take place. It looks like it will start to become mainly dry with some showers from the 23rd onwards and the odd rainy period around the 26th.
This backs up the idea from the JMA 4 week outlook I published back on the Thursday 9th of June.