The air warms up again as it continues on down the east side of the coastal mountains and into the Puget Lowland or Willamette Valley. The air gets warmer because it is under higher pressure at the lower altitudes. Warm air can hold more water vapor than cold air. So even if there is still moisture in the air as it descends into the valleys, the moisture is less likely to condense into rain– it stays “trapped” in the warm air.
This is why the valleys are a bit drier and warmer than the coast– they are in the rain shadow that is cast by the coastal mountains.
The Olympic Mountains block so much rain that the region around the town of Sequim on the northeast coast of the Olympic Peninsula is practically a desert. Cactuses and oak trees grow there in the rain shadow of the Olympics.
The rain shadow of the Coast Range in Oregon (and their Washington counterparts, the Willapa Hills) is not as strong as those cast by the Olympic Mountains or the Cascades. The smaller the mountains, the weaker the rain shadow effect, and vice versa.