= Solution
$F$ is the imposed <radiative forcing>; $-\lambda T_s$ is the restoring change in outgoing radiation; and $-\gamma(T_s-T_d)$ transfers <heat> from the surface layer to the deep ocean, whose equal and opposite gain appears in its own <energy balance>. The additional $-\lambda'(T_s-T_d)$ is a radiative adjustment correlated with the surface–deep-ocean temperature contrast, representing a pattern-dependent effective feedback rather than another conserved interlayer <heat flux>.
For constant forcing, final <equilibrium> has $T_s=T_d=F/\lambda$. During transient warming $T_d<T_s$, so the radiative response inferred from a recent global <energy budget> is $\lambda_{\rm eff}=\lambda+\lambda'(1-T_d/T_s)>\lambda$. If that response were mistaken for the final feedback, the inferred <equilibrium climate sensitivity> would be too small. Summing the two equations makes the distinction explicit: $d(C_sT_s+C_dT_d)/dt=F-\lambda T_s-\lambda'(T_s-T_d)$.
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