Through the circuit. Heat is energy loss.
The heat comes from the resistance. No resistance, no heat. To be more specific, the heat is from the kinetic energy of electrons bumping into the conductive material; no collision no heat.
After a moment, the electrons will be spread out evenly through the wire, right?
So after a moment, the energy that was stored in the system (When all electrons were on the left) is lost.
If no heat is emitted, where did the energy go?
They move over to the other side and back and forth resulting in an oscillator.
That causes all your energy being radiated into the surrounding via radio waves.
That is how your microwave oven works but instead of a superconductor it uses a magnetron with free flowing electrons.
https://www.youtube.com/watch?v=bHIhgxav9LY&pp=ygUVdmVyaXRhc...
It makes it sound like the bulb is getting full power at 1/c, when it wont. As I understand from further reading, the power will build up over time, and that time depends highly on the shape of your circuit.