In summary: standard power supply wiring sucks for Peltier use, so using multiple wires, or replacing them with larger wire and better connectors is the best solution.
I keep reading about Peltier users with hot wiring. This is a waste of vital cooling power! It isn't safe either. There are some things that shouldn't be overclocked!
How many Amps can wiring handle?
I did some digging. The ATX specification is available from:
http://www.formfactors.org/
It specifies Molex connectors, which info on can be found on the Molex site:
http://www.molex.com/
Our power supplies use:
Molex 8981P - Female 4 position housing
Molex 8980P - Female crimp terminal
Molex 8981 - Male 4 position housing
Molex 8980 - Male crimp terminal
The Molex Product Design Specification states:
Current Rating:
14 AWG - 10 Amps (120 Watts at 12 Volts)
16 AWG - 10 Amps (120 Watts at 12 Volts)
18 AWG - 8 Amps (96 Watts at 12 Volts)
22 AWG - 6 Amps (72 Watts at 12 Volts)
Operating Temperature: -10 C to 85 C
A wiring-only rating of a 30 C rise yields 450 Amps/sq cm, which is about 4 Amps on 18 AWG. This is inline with the oft repeated max value of "about 5 Amps" for power supply wiring.
On a typical supply, an Enermax EG651P-VE, the wiring is 18 AWG and rated for 90 C.
Good 50 Amp continuous connectors for 13 AWG can be gotten from Radio Control hobby suppliers under the name of: Astro Flight Zero Loss 2-Pin Connectors. There are other brands too (Deans = 12 AWG, etc.). You'll also find high temperature (>150 C) silicone wire with high strand counts (more flexible and durable).
I'm shopping for a Peltier supply, and will be using thick welding cable (more strands than battery cable, so again it's more flexible) to avoid voltage drop and wasted cooling power!