How does heat flow by conduction?
When part of a substance is heated its thermal energy is increased. The fast-moving atoms or molecules strike the slower-moving cooler atoms. They begin to move faster, and so gain thermal energy. Their temperature increases. The ease of conduction depends on the material. Most metals are good conductors—even a small difference in temperature produces heat flow. Other materials are poor conductors. There can be large temperature differences without significant heat flow. In that case one part of the substance is hot, another cold.
Heat conductivity is higher in metals that have freely moving electrons. So copper, silver, gold, and aluminum are good conductors. Stainless steel is a poor conductor.
In non-metals conductivity depends on their ability to transfer vibrations of the atoms. The conductivity of ice, concrete, stone, glass, wood, and rubber is less than 1/100 that of metals. Conductivity depends on the material, its thickness, the area it covers, and temperature difference.
Light gases have better conductivity than heavier gases. For example the heavy gas argon is used to fill the space between dual-pane windows because of its lower heat conductivity.