Large copper areas on the top and bottom layers are better for heatsinking than a plane on an inner layer, because they have direct contact with the air that is the ultimate heat sink of the system.
That said, an inner layer can reduce the thermal resistance for heat to travel laterally away from the source, and allow the whole copper area of the board to provide some cooling benefit, rather than just the polygons directly connected to the hot part.
Unfortunately the net result, how much cooler will the part be with the added layer, is difficult to predict, or at least requires an expensive 3-d thermal modelling software to predict accurately.
Ultimately it's your judgement whether a modest reduction in the part's temperature (or a modest increase in the temperature range your board can be safely operated in) is worth the expense of increasing the layer count of your board. I'd think that very few situations would justify adding additional layers just for thermal reasons -- normally electrical concerns are what motivates the layer count and any thermal improvement is just a side benefit.