The PCB is actually a quite good insulator thickness-wise. It's... made of layers of plastic.
It's an okay conductor sideways (layers of glass fabric -- mineral, not plastic), which helps keep thinner traces cool. The sideways conductivity doesn't matter much for wide traces and pours, though.
Copper is a few hundred times more conductive, so despite it being a fraction of the thickness of the board, it dominates thermal conductivity. Ground fill is a good idea for this reason, even if you don't need it for EMI purposes!
Even more so, having copper pour on inner layers. If the inner layer is 5 or 10 mils under the surface, that's a lot less insulation, and it can effectively heatsink traces on the surface. This can about double the current capacity of single surface traces. A 20 mil trace might fuse at, say, 10A (I don't know what one typically fuses at), but 15 or 20A with an inner copper plane.
Obviously, this only affects getting heat away from a trace, and doesn't reduce the heat it's actually dissipating. The board overall gets warmer. If you have a lot of traces (or really wide traces) carrying a lot of current in total, all that extra heat makes everything that much hotter, and your total current capacity goes back down.
Don't worry about thermals. They make soldering considerably easier, and have little effect, thermally and electrically. (Calculate it!)
Tim