The highest average temperature in Anchorage is July at 57.8 degrees. The coldest average temperature in Anchorage is January at 14.8 degrees. The most monthly precipitation in Anchorage occurs in January with 0 inches.The Anchorage weather information is based on the average of the previous 3-7 years of data.Loading...he most monthly precipitation in Anchorage occurs in January with 0 inches. The Anchorage weather information is based on the average of the previous 3-7 years of data.