You can see a comparison of those two processors
here. From that you can see that the i7 870 has a TDP (Thermal Design Power) rating of 95W vs. the 73W rating of the i3 540. That would indeed require a higher capacity heatsink to allow for full performance. While the stock i7 870 heatsink would be fine, my favorite Socket 1155/1156 heatsink is the
Intel DHX-B, also known as the
BXXTS100H. It is easy to install, quiet, durable, relatively inexpensive, and has a very high cooling capacity. That unit can handle any processor that fits in those sockets. Scott.