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I'm getting an Antminer V9 soon. I just refer to them as "computers" sorry if that's unclear. But will just the one in my air-conditioned house be fine? Or will I need a whole cooling rig? Bitmain says that it runs at a high of 40c or a little over 100f. Will it overheat without a special cooling setup?

Again, sorry that I didn't say it was an ASIC, haha.
The most issue with ASICs is heat and noise. Maybe you should build a DIY soundproof box (for one only ASIC) and add some DIY cooling systems, you can use Peltier for a small cooling system.