Are faster processors hotter?

Solution 1:

Yes! All else being equal (that's key!), a processor with a higher clock speed will use more energy and therefore also produce more waste heat.

Sometimes manufacturers can redesign a processor in a more-efficient way, or move to a different manufacturing process, or other factors can influence how much waste heat is generated such that faster processor could even use less energy. But, given the critical "all else equal" condition, a faster processor runs hotter and there is a tradeoff between speed and heat/energy use.

In fact, there's a growing market out there for processors that are intentionally underpowered to serve as cpus in computers that don't need great performance.

Solution 2:

The very short answer is YES!

Faster processors will indeed get hotter than a similar processor that is not running as fast.

Something to consider is the advances in materials science over the last 15 years. Much effort has gone into packing more transistors per cm on the chip, reducing power requirements and increases in efficiency which also reduce waste heat. So that being said, know that all processors are not equal at all.