Need to create a magnetic coil (no core) for low frequency field (20Hz-100Hz)
Holy Cow! You're running a kilowatt into a 4-inch coil and you're wondering why it get's hot? Please, rethink this one. 

The reason you can run at higher frequencies is that the impedance of your coil is equal to the resistance plus a term that increases with frequency. Look up impedance and inductance. As your frequency increases, so does the coil impedance, and the total power drops. At low frequencies this doesn't apply much, and that's why you're getting hot.

Increasing the wire size is not going to help. What you need to do is something like this. Wind your coil on a piece of 4" diameter copper pipe, and solder copper tubing all the way around both ends of the coil form, as close to the windings as you can. Then run water through the tubing to get rid of the heat.

Remember, if your amplifier is putting out 1 kilowatt of power, you have to get rid of that power. If you don't heat something like cooling water or air, it all goes into the wire. Just think about how hot a 1 kilowatt light bulb would get.