The highest average temperature in Olympia is July at 64.9 degrees. The coldest average temperature in Olympia is December at 37.3 degrees. The most monthly precipitation in Olympia occurs in November with 10.1 inches. The Olympia weather information is based on the average of the previous 3-7 years of data.Loading...he Olympia, WA pollution index is the sum of the most hazardous air pollutants displayed in pounds. The Olympia, WA pollution index is 23.4% less than the Washington average and 32.2% greater than the national average.