I took Rt. 120 out of Cody directly to Thermopolis which saves some time over the Rt.14/16/20 route through Greybull. From Thermopolis, Rt. 20 takes you through Bighorn Canyon, makes a left in Shoshone and then is a direct shot to Casper. Between Shoshone and Casper, there IS NO terrain. My Swiss cousin described it to his Dad as 'the surface of the moon with grass'!
NO problems at all using that route this past July. If you are driving around Thermopolis town, beware of some low RR bridges but they are usually marked pretty well.
Desolate stretch from Shoshone to Casper: