A cylindrical metal rod with thermally insulated sides is initially at a uniform temperature \(T_C\). At time \(t = 0\), the left end of the rod is placed in contact with a hot reservoir at temperature \(T_H\), while the right end remains in contact with a cold reservoir at temperature \(T_C\). During the transient period before the rod reaches a steady-state temperature profile, how does the rate of heat entering the left end (\(H_{\text{in}}\)) compare to the rate of heat exiting the right end (\(H_{\text{out}}\)), and why?