  It is an ever-growing challenge to develop nano-devices for controlling
energy transport. An open question is whether we can create and control heat
current at {\it strict zero thermal bias}, and if yes, how to do it. In this
paper, we demonstrate that a nonlinear asymmetric system, when pushed out of
equilibrium, can produce heat current in the absence of a thermal bias. The
emergence and control of heat current over a broad range of parameters are
studied. Our results reveal the following three necessary conditions:
non-equilibrium source, symmetry breaking, and nonlinearity. We also
demonstrate that when heat baths are correlated, symmetry breaking is
sufficient to generate heat current.
