Hourly Forecast Detailed. 1  0am:The Eagan, TN forecast for Apr 13 is 45 degrees and Clear. There is 58 percentage chance of rain and 7 mph winds from the Northwest. 2  3am:The Eagan, TN forecast for Apr 13 is 40 degrees and Clear. There is 68 percentage chance of rain and 5 mph winds from the West-Northwest.