You won't be stable at double the clock speed, if that utility is even reporting the clock speed correctly.
From a little Googling, it seems BrazosTweaker tries to change the multiplier (which is locked) and actually seems to trick monitoring programs like CPU-Z into thinking the speed has actually been applied - however, benchmarks show there's no difference, so it's not actually clocking any higher.
I would strongly suggest not bothering, even with a laptop cooler the heatsink itself still won't necessarily be able to cope with the increased heat output, as these netbooks are generally designed to cost as little as possible, so a heatsink able to cope with a faster CPU just isn't necessary as it would just drive up the cost for no gain. Besides, the C60 will never be a high performance CPU.