Space the trenches 12 to 24 inches apart. Sow purple top turnip seeds about 1 inch apart in the trenches, four to six weeks before the last frost for harvest in late spring, covering the seeds lightly with soil. Purple top and other turnip varieties grow best in daytime temperatures of 60 to 65 degrees Fahrenheit. You must plant them so that you have 45 to 65 days before daytime temperatures reach 75 degrees Fahrenheit.