At around 2.6ghz-2.8ghz would extra cooling be needed?
glacio, the short answer to your question is probably not, however, keep the following in mind:
C2D's have nearly 300,000,000 transistors, and every silicon nano-circuit is unique. Each has different basic properties of electronics such as resistance, capacitance, inductance, impedance, and transconductance. Although two consecutive serial number CPU's from the same batch fabrication, with the same stepping codes, may appear identical, they're yielded from different location on the silicon wafer from which they're manufactured, and like diamonds, each has it's own unique flaws.
Even though their dynamic operational characteristics may be very similar, no two CPU's will overclock to exactly the same stable maximum speed, at the same Vcore, at the same temperature. Additionally, in a dual core processor, one core will always become unstable before the other. Successful overclocking is achieved through small increments, and takes a great deal of time and patience.
Check out the following Sticky for info regarding C2D overclocking:
Core2Duo Overclocking Guide v1.1
Also, check out the following Sticky for info regarding C2D temps:
Core 2 Duo Temperature Guide
Hope this helps,
Comp 8)