You will have a slight advantage from stitching, but probably not why you'd expect.
First of all, if the top and bottom copper is carrying equal current, then heating will be equal, period. That's a simple setup, and if your situations fits, then the following will apply.
Trace temperature rise is limited by heat loss. Ultimately, the only heat loss is convection (or radiation or conduction) off the board surface. If the board is in free, still air, then it's around 150 in^2*C/W (yes, a horrible bastard of a unit, I know) for all surface area.
If you have a single trace (well, in this case, one on each side, but in the same location), and nothing else on the board, you get heat dissipation from the area of the trace itself... but also, the heat spreads laterally a modest distance, and the board itself helps out with heat dissipation.
Now here's the kicker. PCB is more conductive laterally (in-plane) than depthwise (through-plane). If you just have trace on the surface, only the surface of the PCB carries heat sideways. The core, even right in the middle, may be cooler than the traces, because the core layers conduct a farther distance.
Now, if you stitch this construction with vias, you have quite a bit more through-plane conductivity. This carries heat to the core, and the heat spreads a somewhat larger distance, reducing temperatures overall.
It's more pronounced with inner copper layers, which can be pierced (or joined) with vias, and carry even more heat sideways than the laminate itself.
Of course, the advantage also goes away if you are using the whole board to carry current. That is, if the whole board is getting hot, there's no spot that's cooler, for heat to spread out into. The temperature is largely similar to the expected case, based on copper resistivity, and PCB dissipation capacity.
Tim