An electric iron controls its temperature automatically by making and breaking the current to the heating element, and the part that performs this switching is the thermostat.

The thermostat is built around a bimetallic strip, two metals with different rates of thermal expansion bonded together, which bends as its temperature changes.

As the soleplate heats up to the set value the strip bends and opens the contacts, cutting off the current so the iron stops heating.

When the soleplate cools slightly the strip straightens, the contacts close again and the current is restored, so this repeated on-off action holds the iron near the chosen temperature.

The heating coil is only the source of heat; it converts current to heat but does not decide when to switch, so it cannot regulate temperature.

The soleplate is the metal base that stores and transfers heat to the cloth, and the indicator lamp merely shows whether the iron is on; neither controls the current.

Hence, the answer is Thermostat.