From what I can see during heating and use is the heater is like what you can see in a toaster. Flat wire wrapped around in a coil/circle form. That's only when it's red hot for for the heater. Can't be 100% sure.Since the soldering iron has no laminations the noise is produced by some other mechanism. If the element is a helix of resistance wire then adjacent turns tend to repel each other as a result of curent flow. This could cause mains-frequency vibration.