Core i5 4460 Running a Little Hot

I'm not too familiar with mPrime, but if it's running AVX instructions like other versions of Prime95 aside from version 26.6 do, then those thermal results are likely unrealistic. Is this a Linux only machine?

Prime is a completely unrealistic test that maxes out every single part of the inside of the chip. 90c is tmax, so you are fine!

Spend the $25 so you don't have to hear that thing whir away all day?

REALLY? A 90 dollar fan is "the cheapest thing with a decent copper plate surface"? C'mon, be real.

You don't need anything like that. A half decent aftermarket cooler that will run you about 35 bucks, like the Cryorig H7, would be fine. If you wanted to step it up, you could do much worse than going with the Noctua NH-U12S or U14S.

Buy the Noctua fans. You don't necessarily need PWM models, as 3 pin voltage controlled models are fine, but the PWM models MAY allow you to drop the minimum speeds a little lower than a voltage controlled model and MAY be slightly quieter overall. What you WILL get are fans with much better bearings that are STILL quieter after six months. A lot of cheaper fans that have equivalent decibel levels on paper when new, to the Noctua and some of the other fans, WON'T still be that quiet after a few months of use. They won't last as long either. You'll be replacing a Cooler Master Sickleflow fan three times before you have to replace a Noctua fan, at least.

Plus, premium fans like Noctua are able to maintain that low decibel level while moving a significant amount of air while most your budget entry level fans can only claim low noise levels by creatively orchestrating tests at lower RPMs or using voltage reduction filters inline, and specifying the max decibel level of that configuration. Premium fans like Noctua, Phanteks, Thermalright, Noiseblocker, Scythe and a few others, are standard go to products for a reason.

If you just need something for the NOW, it probably is fine to go with a less expensive product. If you want something of high quality that's likely to last the life of your build, or at least far longer than any 8 dollar fan, then you'll want to pony up the extra money.

Now, to address that other nonsense. Prime is NOT a completely unrealistic test, UNLESS you're not using the correct version for thermal testing which is version 26.6. That version does NOT use AVX instructions and IF you test using Small FFT you will get the absolute best method of providing a steady state thermal load that any current utility is capable of providing. I'll be more than happy to back that up with a plethora of supporting documents and opinions, including that of our own CompuTronix who wrote the Intel temperature guide.

For Linux though, as I said, I'm not too familiar with mPrime, but I'm going to check with CompuTronix to see if there's an mPrime version that does not use AVX so you can get a realistic thermal limit test that's trustworthy. Although you haven't exceeded the TjMax or Thermal trip specifications, for a stock chip, yours is warmer than would be expected, except that you ARE still using the stock cooler.