I would build the power supply in the unit, so only one cable goes to the wall outlet and everything else is inside the unit. You can purchase ready made switching power supplies that weigh next to nothing and provide any voltage @ current you need. This is a lighter weight alternative to transformer and linear power supply. If you use a transformer you will also need a rectifier, capacitor and probably a voltage regulator, maybe a heat sink. All of a sudden space and weight have grown. Of course if you only need a few milliamps you can use a small transformer and the other components don't need to be very big, but if you need more than an amp or two, a switching supply is the way to go.
Search Jameco , Mouser, McMaster-Carr, Thomas Net, etc. for the supply you need. Many come with DIN rails and screw terminals for input/output connections. Be sure to include fuses in your design, at least two: one for the heater and one for the electronics. They can save your house and life. When you are dealing with 1000W heat source it will get hot. Also it will be drawing at least 8.3A (1000/120) so make sure you use a large enough power cord 16awg or bigger.