Late May, should be great riding weather. Days should be warm, but I would think you will run into scattered showers somewhere along this route. Not sure about the north end, but expect bugs on the south end. Enjoy the ride.
Nashville: Natchez Trace... 78 and windy yesterday, tornado's last night, 43 and cloudy today... Don't lke the weather, just wait 2 hours and it will change... May should be great weather on the trace but be ready to run over a bicycle or two...