On my K7S5A, I get CPU temperature readings of up to 59C with a 1GHz Duron overclocked to 1.33GHz, which is approaching the 1.4GHz that your 1600+ runs at. Mine is one of the original-revision K7S5A's. Anyway, it runs quite happily at that temperature.
I wonder if your motherboard's chipset is overheating, since I have heard rumors to that effect with K7S5A's. I see in your other thread that opening the case and aiming a fan into it fixed the lockup problem, so keep this in mind as a possibility. While you're waiting for your Alpha to arrive, maybe you can test this theory by putting a little fan on your motherboard's heatsink, if you have one lying around.