You can't mine bitcoin with a computer. You'll end up spending more in electricity than you'll ever earn in bitcoin.
If you want to mine bitcoin, you'll need specialized ASIC equipment.
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.