Final answer:
The term describing the process of mantle material rising when heated, moving laterally when cooled, and sinking when dense enough is Plate Tectonics. This process is a result of convection within Earth's mantle, essentially acting as the planet's cooling system.
Step-by-step explanation:
The term that describes the process you're referring to is Plate Tectonics. This theory explains how slow motions within the Earth's mantle move large segments of the Earth's crust. This process leads to a pattern of rising and sinking mantle material. As the mantle material heats up, it rises and then moves laterally when it cools. Once its density is high enough, it sinks, making room for more warm material to rise, thus repeating the cycle.
This process is due to a phenomenon called convection, which is the movement within a fluid (in this case, the semi-fluid mantle material) due to the tendency of hotter and therefore less dense material to rise, and colder, denser material to sink under the influence of gravity. This sequence of events results in the transfer of heat.
Through Plate Tectonics, the Earth efficiently transports heat from the interior, where it has accumulated over time, out to space. It is a cooling system for the planet. This large-scale geological feature of the Earth is crucial to its constant evolution.
Learn more about Plate Tectonics