In the lumped system analysis the temperature of a body is uniform throughout the body at any time. But the temperature of the body as a whole can vary with time.
That means the thermal conductivity of the body has to be higher so that the heat can readily transfer throughout the body. The temperature of the body varies along with time.
So, suppose a heated copper ball is suddenly dropped into an oil bath (for quenching or other heat treatment process) it is assumed that the temperature of the copper ball remains uniform throughout and changes with time.
But, Sometimes it is difficult to assume the temperature to remain uniform throughout because the system may not satisfy the lumped system analysis criteria. A body with low thermal conductivity can not immediately transfer heat throughout the body because it has high internal conductive resistance.