I just finished dealing with a similar problem on my 289. I installed a new 190 t-stat, shroud and 6 blade flex-fan and solved the problem. My location is SE Texas and the dog days of summer also. Now it will idle under the carport at 190. I didn't notice what year your Jimmy was but is there room for a shroud in your set up? If so, I highly recommend it.

Also, when my t-stat opens the temp drops to 170 and then eases back up to between 185 and 190.