What is the meaning of “in a medium” in the following sentence?
A major objective in a heat transfer problem is to determine the temperature distribution in a medium resulting from imposed boundary conditions on the surface of the medium.
In this context (it reads like something out of a thermodynamics textbook perhaps?), "medium" simply means "substance" or "material", maybe a pool of water or a block of iron.
the intervening substance through which impressions are conveyed to the senses or a force acts on objects at a distance.
Heat is first absorbed from the source by an intermediary substance that subsequently transfers it to another material. This process is technically referred to as heat-transfer. The substance acting as an agent in the middle is known as medium in this context.
Any solid or fluid (such as water, steam, air, or flue gas) which is used to convey heat from a heat source (such as a boiler furnace), either directly or through a suitable heating device, to a substance or space being heated.