A thermal paradox: which gets warmer?

In this paper we address a common misconception concerning the thermal behaviour of matter, namely that the front surface of a very thin plate, uniformly illuminated by a constant light beam, reaches a higher temperature than the front surface of a very thick slab made out of the same material. We present analytical solutions for the temperature rise above the ambient of thin and thick samples, after a heating lamp is switched on. It is shown that the temperature rise at the illuminated surface of the thick sample is twice that of the thin plate. However, the temperature rise of the thin plate is much faster (minutes) than the heating of the thick one (hours). This explains why our intuition, which learns from what happens at the very beginning of the process, leads us to the feeling that the front surface of a thin plate will get warmer than the illuminated surface of a thick slab, i.e. the above-mentioned misconception.