What OlyAR15 said.
The cooler with fan that Intel bundles with its processors is designed for -- and varies with -- the particular processor model. So an i3 processor will have a light-weight aluminum heatsink; an i7-4790K will have a heatsink that almost looks the same, but has a much heavier copper core.
Intel is very meticulous about their products. Each retail-box processor is rigorously tested with three batteries of tests before packaging. If you visit the Intel web-site, you will find hundreds of pages describing every detail of your processor. Intel knows with a dead certainty the speeds, voltages and thermal limits of its processors.
so the processor should run at its spec settings with the stock cooler. Not enough for you? Then provide better ventilation and air-flow within your case.
Here's an example pointing out the limitations of the stock cooler. I acquired an (old!!) i7-2700K retail-box processor. I decided to test it with the cooler that came with it. It has a turbo-speed of 3.9 Ghz.
So I tried raising the clock-speed to 4.2 Ghz without changing the voltage. I could see that the processor could provide that speed on "auto" voltage. But then, I ran the OCCT "CPU:OCCT" stress-test. It took a couple minutes before the test terminated on its own. It did this because the temperature had risen to 87C, and apparently OCCT defaults had imposed that limit.
Then, I mounted my EVGA ACX heatpipe cooler. 4.7 Ghz, CPU:OCCT shows about 64C under stress-load.
It all depends on what you intend to do with the system. As long as you run the processor at stock settings, it should take everything you throw at it. If you choose to do something else like overclocking, you'll need a better cooler like the men in "Jaws" "need a bigger boat." And you'll need to use a case that provides space for the cooler.
There ARE some low-profile coolers that should be an improvement over the stock Intel HSF. I just wouldn't waste time and money unless you want to do "K" stuff with a "K" processor.