In most years, Key West averages a daily maximum temperature for June that's between 87 and 89 degrees Fahrenheit (30 to 32 degrees Celsius). The minimum temperature usually falls between 78 and 80 °F (25 to 27 °C).The days at Key West warm slightly during June.lear skies. The sun's rays reach the ground in Key West during 76 percent of daylight hours on average in June, for a total of 311 hours in the month. Typically on 5 days this month the sky is mainly clear, with at most 30 percent cloud cover. Sunlight in June at Key West averages 13 hours and 38 minutes a day.