A wire heater may not be what you're looking for. There's a fine line between bending styrene and melting it, so you want to make sure you have accurate temp control.
I know there are tools made for bending acrylic, which may be a better starting point than a typical 'hot wire', which is more often used for cutting than bending.
Or, if you really want to get fancy, why not consider doing some vacuforming. Form up a wooden plug mold, and you can use that to make compound curves and all sorts of tricky shapes that you'd be hard pressed to form plastics into normally.