Thermal conductivity are often used for surfaces between the computer chip and the heat sink to increase heat transfer and they want high thermal conductivity to decrease the thermal resistance. By $$\Delta T=RQ$$ and $Q$ is constant by the chip. When we decrease R, and keep Q constant from the chip, we decrease $\Delta T$ between the chip and the heat sink.
This is where I get confused because I assumed we would want the temperature difference between the chip and heat sink to be as high as possible. If the two temperatures are close to each other then wouldn't that make the chip heat up and exceed the operating temperature? I thought we would want the heat sink to be much colder than the chip so the chip will cool.
Can someone clarify?