  Situations where a spontaneous process of energy or matter transfer is
enhanced by an external device are widespread in nature (human sweating system,
enzyme catalysis, facilitated diffusion across bio-membranes, industrial heat
exchangers). The thermodynamics of such processes remains however open. Here we
study enhanced heat transfer by a model junction immersed between two thermal
baths at different temperatures $T_h$ and $T_c$ ($T_h>T_c$). The transferred
heat power is enhanced via controlling the junction by means of external
time-dependent fields. Provided that the spontaneous heat flow process is
optimized over the junction Hamiltonian, any enhancement of this spontaneous
process does demand consumption and subsequent dissipation of work. The
efficiency of enhancement is defined via the increment in the heat power
divided over the amount of consumed work. We show that this efficiency is
bounded from above by $T_c/(T_h-T_c)$. Formally this is identical to the Carnot
bound for the efficiency of ordinary refrigerators which transfer heat from
cold to hot. It also shares some (but not all) physical features of the Carnot
bound.
