It needs to be decently thick, and copper wire definitely doesn’t have nearly enough cross-sectional area for this.
Here’s an example of a good thermal path. The MCPCB rests on a shelf that, along with the entire head of the light and heatsink fins, was machined out of a single, contiguous piece of metal. You can get away with less material due to lower power, but this is the ideal type of design.
Source.