I think it depends on the motherboard for the most part. Let's take the well-received Abit NF7-S 2.0 for example! In BIOS, there's a setting that is basically "do you want the PC to turn off if the CPU fan fails?" I tried it out last night, and it works VERY well.
The moment the CPU fan is getting no power, the PC shuts down.
Now, if the CPU HSF were to fall off and remain plugged in, that could be a problem. I've never heard of a processor-based thermal shutdown (even on P4's), so that's new to me. I really don't think Athlons have it. But like I said before, I didn't even know P4's had an onboard thermal shutdown.
Either way, in most motherboards, there's a thermal shutdown temp AND a CPU failure safety kill switch, so I see that as adequate thermal protection. If the processor gets too high, it shuts down. If the CPU fan breaks, it shuts down. If the CPU fan falls off and remains plugged in, then the heat will probably kick in the BIOS temp thing and it'll shutdown as well.
I usually make thermal shutdown temp at 70-75 celsius. The default on mine is 110 celsius, but I think that's a bit too high.
So basically, the only way the absence of a non-processor thermal control is if the motherboard thermal shutdown didn't work. And from my experiences, they work very well.
-Lasereth