Replace the term GROUND plane with copper plane... it is any copper plane will HELP dissipate heat. There is more to it and thermal management can get very interesting... Also because of the limited thickness of PCB copper planes the distance the heat can spread from a heat source is limited, the higher the copper weight the further the heat will travel though. Without digging out my info I believe it is about ~40mm for 1oz copper.
But as copper is a far better heat conductor than FR4 the planes help dissipate heat through the Z axis...
Then you get onto thermal vias.
IPC-7093 is a good read and a search for PCB thermal management should provide hours of happy reading material.