what happens to convection currents when a fluid reachesa constent temperature?

Question

science subject

Answer 1

"Convection is the transfer of potential energy, for example heat, by currents within a fluid. When a portion of a fluid is less dense, it rises due to gravity. By rising, it displaces an equal volume of the same fluid which flows to occupy the space left unoccupied by the less-dense portion of fluid which is rising. This causes a closed loop flow, an internal current inside the fluid.
For example, when water heats up slowly in a pot on a stove, it appears to warm up almost uniformly. Heat penetrating from the bottom of the pan warms the closest water via conduction and radiation, and this warmed up water being less dense, rises, and allows cooler water to come down to the bottom of the pot. While rising, the warmer water transfers some of its heat to the water in the middle and at the top of the pan. Once it cools, it becomes denser and sinks, going back down to the bottom, where it picks up heat and continues the process."

So my guess is that if the temperature within whatever medium was being affected stabilizes or reaches a constant temperature throughout, the convection process would come to a stop, since there is no temperature difference between areas. Temperature differences are necessary for convection to begin or sustain itself.