I wonder if you can use radiant heat wire?? I have installed these wires in driveway's before its covered in asphalt or concrete. They are used to prevent freezing on slippery driveway surfaces. There installed in a zig zag shape running across the surface. You could look into it, the wire would be arranged around the root area a few inches underground, although you need to bring power to them. Hope this gives you some idea...