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6 core processors

Than quad cores? No
Than octa-cores? Yes........

It all depends on what you're comparing it to. A ryzen is going to be cooler than a quad Intel Nehalem processor for example and many other factors can play as well
 
Mine doesn't. It runs oddly cold for some reason. Its not due to water cooling alone. These Broadwell chips run cool. Sandy-E took more cooling muscle than their quad core counterparts. With the advent of toothpaste TIM on newer quad cores, the enthusiast line runs cooler than the quad cores these days from what I can tell. There is no straight answer to your question without considering what generation of chips you are referring to. If all else is equal, then yes a 6 core will run hotter than a quad simply because there's two extra cores putting off heat. Things aren't equal these days though.
 
My Ryzen 1700 runs about 10C hotter than my i7 3930k.

Realistically though. If you have the exact same die (like Ryzen) and you can disable it down to 4c and 6c from the 8c it came as. Then the 6c at the same work load would use more than 4c and the 8c over the 6c. For two major reasons one, even if if a core is not in use, it is still running at a marginal speed and still uses some power and second because it is actively being fed power (and generating heat) it is no longer acting a as a "black" area on the die wicking heat to be fed to the heat spreader (I know I am not describing that right). There is more that electricians in here can probably describe and you also have to take stock voltage and target TDP into the equation as well.
 
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