Maybe you can bring a parka. 

In some places the difference could be double digits

According to the Washington Post, areas where the eclipse reaches totality will see a sudden drop in temperature.  The Post tells us nighttime cool downs are gradual.  The eclipse brings sudden darkness.  In some places, the difference could be double digits in a matter of a couple of minutes.

While this would be a concern in winter, most people watching in Idaho will likely appreciate the brief chill especially following a hot summer.