Question

Why does a metal bar appear hotter than a wooden bar at the
same temperature? Equivalently it also appears cooler than wooden bar if they are both colder than room temperature.

Answer 1

The rate of transferring heat in metal (due to free electrons) is larger than that in wood, or we can say that the conductivity of the metal bar is extremely high as compared to the wood.
Also, the specific heat of metals are lower than any wooden bar. So, the metal needs a very small quantity of heat to change each degree of temperature.

Thus, due to larger conductivity and smaller specific heat, metal appears colder and hotter than wood when kept in cold and hot regions, respectively.

Final answer: Due to larger conductivity and smaller specific heat capacity of metals.