Have you tried replacing the Thermal Paste?
You should be doing this ideally every 6-18 months depending on how much Demand you put on a Processor...
For example just running it Stock and doing nothing but Normal Desktop stuff with < 7hrs of Gaming a Week; you should be looking at 12-18 months replacement., but if you're playing more and "Overclocking" then you're going to want to ensure you keep on top of replacing it as often as possible; along with removing all excess dust.
More often than not, just doing said regular maintenance will bring System Temperatures back to something more reasonable.
Now as for how well the H410i Performs., it's "OK" but won't really offer much over the Packaged AMD Cooler (which is rated for 95w) … although it'll do that keeping quite High Temperatures (75c typically) and fairly loud.
It's likely the H410i will probably reduce that to maybe 70c., but the Hyper 212 EVO even in Single Fan Configuration (which as a note I have one in Dual Fan Configuration on an A10 7890K overclocked to 4.8GHz Core / 950MHz GPU, maintaining 62c) should easily keep an A8 6600K at < 65c near silent.
What makes them good., is their Vapour Chamber and Copper Heat Pipes (without any "Stylistic" Nickle Plating that somewhat lowers efficiency)
All CoolerMaster Coolers come with an Adjustable Bracket., which supports everything except AM4/TR4 Sockets; for those you'll have to send off for an kit; that used to be free but no idea today.
Still, as I initially said; just replace the Thermal Paste (Kryonaut is good) and clean out all the Dust., it'll almost certainly be enough. At this point I'd recommend looking into a Full Upgrade., to either an Athlon 200/300-Series or Ryzen with Graphics (2200G/2400G)
I mean it'll make a MUCH bigger difference for Gaming.
Even the 2-Core / 4-Thread / 3CU GPU, Athlon 200GE (£47) essentially will double your performance... go for something like the Ryzen 3 2200G and you're getting 4-Core / 8-Thread / 8CU GPU., essentially Minimum Specifications for most Games today.
