Hot Springs will definitely be 'hot'.
I don't know your timing but have you done much in Colorado or northern New Mexico? I think once crossing the Plains states I'd head for much cooler temps rather south into St. Louis/Arkansas.
- northern New Mexico: take Hwy 64 off I-25 which will take you to Cimarron, Eagle Nest, Red River, Taos and then down to I-40 to Arizona 191 or 77 and spend time in Springerville, Eagar, Greer, Pinetop, Show Low before taking 60/77 south into Tucson.
- Colorado - come in on Hwy 50 or 160 and head west of I-25 - many nice 'cool' towns to explore. To get to Tucson take 160 to Cortez, CO then south on 160 into Arizona and west to 89 and south into Flagstaff and head south to Tucson.
Full-timed for 16 Years . . . Back in S&B Again
Traveled 8 yr in a 2004 Newmar Dutch Star 40' Diesel
& 8 yr in a 33' Travel Supreme 5th wheel