If I run the speaker wire under the carpet it is 16 gage wire, could it get overheated and start a fire? Sorry I don't know much about wires, I don't think it will but want to make sure don't want to burn the house down.
The main consideration is where it's routed. If it's in a traffic area, it can eventually get stepped on enough to cause problems with shorting or broken conductors. Not that that's a fire hazard with speaker wire, but it can cause troubleshooting fits if you don't think about it.