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It puts out 65W of heat and it's an LGA1151 socket.
You can get something like this for it:
https://www.quietpc.com/mugen-5-pcghWhich will take the CPU fan down to 15 dBA at peak.
There's no mention of a GPU, so I'm guessing you're using the onboard on the motherboard https://www.gigabyte.com/Motherboard/GA-Z170-HD3P-rev-10
I think you should be fine to get a big case that could take a larger CPU heatsink and achieve total silence.
The only other fan in your system appears to be the PSU:
https://www.evga.com/products/product.aspx?pn=120-G1-0650-RXSomething like this: https://www.quietpc.com/fsp-hyper-m?product=5375
This is only 600W, but without an optical drive or GPU... you don't need 650W.
With a new CPU heatsink and a new PSU and a case, the entire system would be under 20dBA (basically virtually unnoticeable).
This it’s what’s in there (apart from the P/S and plus a EVGA GTX 750 Ti SuperClocked 2GB GDDR5) - I remember being impressed at how cool it ran when new but I haven’t checked for years.
I don’t do much gaming so doubt the graphics card fans are kicking in - it’s all system fans.