Wire Gauge for STC-1000 build

[aprichman]

Looking to build an STC-1000 (inkbird) temperature controller. I've got an old computer power cord that I was hoping to use that's labeled 18AWGX3C. The controller would be used to drive a brand new (energy efficient) 5.1 cu ft chest freezer.

The black, green, and white wires on the inside have no markings on them.

Basically I'm looking to build this as cheap as possible but don't want to burn down my apartment.

 

[Ravenshead]

18 AWG might be a little light but it's close. I'd use the same gauge wire that the freezer uses.