Wire size is determined by the CURRENT flowing through the wire, not the voltage. Wire rated for 12 amps intermittent duty is probably 20 guage. For 15 amps the wire size should be 18 guage.
This is why high tension wires run such high voltages. Work is measured in WATTS which is volts multipled by amps. 20 volts at 1 amp produces 20 watts of power. So does 10 volts at 2 amps-or 100 volts at .2 amps.
BUT the 100 volt transformer only needs wire that can carry .2 amps, (30 guage or less) while the 10 volt one needs 22 guage. Since every time you reduce the guage by 2 numbers it gets twice as thick, you'll be using wire that's 16 times thicker then the 100 volt wire. for the 10 volt one.
On the other side, a million watts can be made by running a half million volts at 2 amps or running 10 volts at 10,000 amps. Now you understand why interstate high tension lines are usually a half million volts or more.