What term describes the rising of cold water from deeper layers to replace warmer surface water?
Stirring, if you are referring to a laboratory experiment.
Upwelling, if you are referring to large lakes or oceans.
The only way for cold water to rise to the surface of any non-agitated container is stirring by whatever means will provide the result.
Upwelling is the result of winds and earth's rotation, and I suspect that rising tides due to the influence of the moon could have some effect.