Whilst far from guaranteed, there is a reasonable chance of rain throughout much of Thailand in June. Temperatures remain high (avg temp: 29-31°C) and, at least initially, the rain is likely to come in the form of short downpours, with periods of good weather expected throughout much of the day.
In the north and central regions, the rainfall begins to bring some green-ness back to the hills and rural countryside, and some depth to the rivers and waterfalls, although slightly muddy conditions can be expected if you plan on trekking in the Golden Triangle region.
Weather patterns in the south and on the islands are similar to May. Khao Sok National Park is warm and wet, although humidity levels have dropped slightly. Koh Chang and Koh Kood are particularly wet and there is a high chance of rain on the west coast beaches of Phuket, Khao Lak and Krabi. For guaranteed sunshine, Hua Hin & Cha Am and the east coast beaches of Koh Samui, Khanom and Koh Pha Ngan are the pick of the bunch, with little, if any, rain expected. Favourable dive conditions continue around Koh Tao and the east coast islands.