Some peculiarities of the heat transfer through a sample that is heated by the superficial absorption of light energy under continuous uniform illumination are discussed. We explain, using a different approach to that presented in a recent article published in this journal (Salazar et al 2010 Eur. J. Phys. 31 1053?9), that the front surface of a thick sample reaches a higher equilibrium temperature than a thin one, a fact that may be against some people's first intuition. From the analytical solution of the problem, we obtain a condition necessary to apply a very thermally thin sample approximation, i.e. to neglect a temperature gradient across a sample. From the analysis of the heat transfer through both a thermally thin and a thermally thick sample, we suggest an inexpensive experiment suitable for measuring the thermal diffusivity of low thermal conductivity solids. Both the theoretical analysis and the suggested experiment can be suitable for students and teachers dealing with heat transfer problems, thermal characterization techniques and/or partial differential equations at undergraduate and graduate levels.