This is the reason hot air balloons work, and why the cold water is near the bottom of the lake and not on top. This process also drives the major wind patterns. Rock is no different, and when heated it lowers in density and wants to go up. So far so good. The problem is that if it rises it's going to leave a void where it was, and we sure can't have that.
Most geologists accept convection currents as the most likely mechanism for plate motions.
One of the biggest questions now relates to how deep within the mantle the convection cells extend. Many geologists favor this concept. Many others favor shallow mantle convection. Others postulate multiple layers of convection. And I know 3 big boys in Grants Pass who are still looking for a rope.