Through much of the middle portion of the week, there will be a broad upper level trough over the eastern U.S. with a few small troughs that ride around the larger trough. The main impact of this trough for Middle Tennessee will be to push the deep moisture east of the Appalachian Mountains, and keep temperatures fairly cool in Nashville. A secondary trough passage will occur on Friday, but there will be a lack of moisture that makes the chance of rain very low. Friday will have some partial cloud cover, and there is one model that generates some rain, but at this time I think a dry day is most likely.
Nashville will be on the west side of the trough on Saturday, which will keep dry weather and mostly sunny skies in the forecast. With a high pressure ridge slowly building in, temperatures will trend upward into the lower 90s by Sunday. Humidity levels will be rising too, but dewpoints are expected to be in the upper 60s to near 70, which could be much worse for this time of year in Nashville. The normal high for Nashville this time of year is around 91, so we should see highs in that neighborhood.
I'll be attending the race this weekend. As a resident of Tennessee, it's exciting to have a race in my home state!