If you're not planning on overclocking, it's good enough to keep your 1.2GHz athlon stable for probably as long as you'll use it. Just ask if you're still planning on using your current machine in 5-10 years. Better cooling may extend the life of the chip but may not be worth the cost if you're only keeping it for a couple years. Now if you overclock, you definitely need a better heat sink/fan or you'll experience a very short lifetime.
I agree. That stock fan will cool well enough to use everyday. If you get any lockups, most likely you'll need to add a case fan from radio smack. A little arctic silver will let you overclock stably, but not much (50mhz). Either way, everything is just a guess as to how long the processor will last. I'm guessing from my past machines, and hoping the trend has continued.
I sincerely suggest that you AMD gurus give Sigma pointers as to mounting the heat sink to prevent damaging the T-bird's core!
I'm a P3 user myself so I don't know T-bird installation "do's and don'ts", but my brother (who had previously built a P2 system), recently tried building a new AMD system and wound up cracking the T-bird's core while mounting it! He still doesn't know where he went wrong.