The average daily low temperature in Colorado Springs on June First is 46 degrees Fahrenheit and the average low on the last day of June is 56 degrees.Colorado Springs usually receives an average of 2.34 inches of precipitation during June.istorical weather data accumulated by the National Weather Service shows that the average daily high temperature in Colorado Springs on June First is 72 degrees Fahrenheit and the average high on the last day of June is 84 degrees.