Rather than use Auto-Tune, I decided to overclock the old-fashioned way, set the clock and see how the HD 3850 performs by running a couple of benchmarks, to check for stability and performance. I have found from experience that a GPU's performance starts degrading due to too high an overclock long before it crashes. That experience causes me to wonder sometimes about factory-overclocked cards, such as an 8600GT I have. It feels like it is overclocked too high, but I never have the time to lower the clock rate to see.
After a fair amount of experimentation, I find that 685 mHz is the max before the performance starts falling. As I mentioned earlier, I didn't play around much with the memory clock. I just cranked it up to 849 mHz and left it there. Not a lot of overclocking to be done with the Apollo HD 3850 for sure.
I was impressed with the GPU cooler, as well as the GPU itself, as far as temperatures go. With all of the overclocking and testing, the GPU never got over 50C. Both of my nVidia cards idle stock at over 60C with the stock coolers.