The discussion revolves around calculating the heat transfer rate through a plane wall with variable thermal conductivity defined by k(T) = k0(1 + βT). Two methods are explored: one using an energy balance approach and the other applying Fourier's law directly. Both methods lead to the conclusion that the heat transfer rate, Q̇, can be expressed in terms of the boundary temperatures and the thermal conductivity function. Participants also discuss the implications of varying the coefficient β, noting that gases typically have a positive coefficient while liquids and solids often have a negative one, with water being an exception. The conversation highlights the importance of correctly applying boundary conditions to derive accurate results for heat transfer calculations.