A cylindrical metal rod of uniform cross-sectional area \(A\) and length \(L\) is thermally insulated along its sides and connects a hot reservoir at temperature \(T_H\) at position \(x = 0\) to a cold reservoir at temperature \(T_C\) at position \(x = L\). The system has reached a steady state of heat transfer, and the metal has a thermal conductivity \(k(T)\) that increases with increasing temperature. Which of the following correctly describes the graph of temperature \(T\) as a function of position \(x\) along the rod, along with the correct physical reasoning?