  A mechanism of electron-mediated pumping of heat in the absence of net charge
transfer is proposed. It may be realized in charge-neutral electron systems,
such as graphene, coupled to an external electric potential. The flow of heat
in this pumping cycle is not accompanied by a buildup of voltage along the
system, which offers advantages over traditional thermoelectric cooling setups.
Efficiency of heat pumping and magnitude of heat flux are studied in the
hydrodynamic regime for weak disorder. In a pristine system, even for an
infinitesimal pumping potential the heat flux remains finite. In particular,
for a potential in the form of a traveling wave moving with velocity $c$ the
pumping is perfect; the entire heat content of the electron liquid is advected
with velocity $c$. For a general pumping cycle the heat flux is determined by
the cycle geometry and disorder strength.
