I will quote what Tom's said about this:
"Cooling is a naturally an important consideration, then. Intel says that its RTS2011AC air cooler, which sells for just under $30, is not sufficient for the Core i7-3970X. However, the RTS2011LC closed-loop thermal solution we’ve been using for testing is able to handle 150 W CPUs. Since many vendors don’t get specific about their thermal performance, you’ll need to check with your vendor of choice about compatibility. And because Intel doesn't ship its LGA 2011-based models with coolers, plan on spending $70 to $80 more for something appropriate."
So I would say you will be fine, at stock clocks of the 3970X.
The 3970X really isn't much more power hungry than the 130W TDP chips, Xbitlabs said that the main reason for the TDP increase is to make room for even faster chips for the 2011 platform eventually:
"Of course, if you feel like shocking anyone with your power consumption numbers, then maximum load is the way to go. This is where Core i7-3970X is the one and only leader. Its power consumption is so high that it not only puts the system with AMD FX-8350 to shame, but also more than doubles the power readings of the LGA 1155 configuration with a Core i7-3770K. However, the power consumption difference between the system with the new Core i7-3970X and the system with the Core i7-3960X still doesn’t reach 20 W – only 12 W. In other words, the newly declared TDP have some reserves for yet another frequency boost allowing for even faster six-core Sandy Bridge-E processor to come out one day."