Lets start wit hthe studff you should have learned in school:
> Would 3 rigs create much more heat compared to one?
Yes, like... THREE TIMES. See, if one rig uses 1000 watt then three rigs use 3000 watt and as tehy dont magically get more efficient, they also generate three times the heat
And three times the noise.
The problem will be the heat - there is a limit what you can handle. I am right now settgin up three experimental rigs in my appartement, distribute in diferent places thanks to me currently not being there for some months
While looking for a room to put some dozen servers. Like edecdicated - without having a special room you are limited. Power amounts go to levels not ok for normal house wiring, cooling gets bad, noise gets bad.