A metal gets cold or hot faster when compared to a block of wood because of its high thermal conductingcapability. The metal has a small energy band gap. Hence electrons can quickly jump up and down according to the given conditions and the energy of the electrons that are on the edge of the bands.
Wood has a low thermal conducting capability than metal as it is considered an insulator. Wood has a high energy band gap. Hence, it is not easy for the electron to gain that large amount of energy and move into the conduction band or lose the same amount of energy and move back to the valence band.
When both materials are at the same temperature due to the different nature of conductivity, the metal will take energy from the surroundings, and wood will resist it. Thus even though the surrounding temperature is the same, they both will be at different temperatures.
A hot block of metal means that metal has received more energy, and the available electrons will have more energy; due to the higher thermal conductance, they will transfer the same energy to other electrons, and collision and other activities will increase the thermal energy. The exact process or activity will not happen in the wood due to the lower conductance.
There is no such temperature where metal and wood feel the same due to the difference in thermal conductivities.
Thus, even though they are at the same temperature, both material metal, and wood; metal will feel colder/hotter, and there is no temperature at which they both will feel equal hot or cold.
