  We develop a theory of fluctuation-driven phenomena in thermal transport in
graphene double-layers. We work in the regime of electron hydrodynamics and
focus on the double charge neutrality point. Although at the neutrality point
charge transport is decoupled from the hydrodynamic flow, thermal fluctuations
of electron density cause both drag and heat transfer between the layers. The
thermal transport in the bilayer system is governed by these two phenomena. We
express the drag friction coefficient and the interlayer thermal conductivity
in terms of the interlayer distance and the intrinsic conductivity of the
electron liquid. We then obtain the thermal conductance matrix and determine
the spatial dependence of the hydrodynamic velocity and temperature in the
system. For shorter system the thermal drag resistance is determined by drag.
In longer systems the situation of perfect thermal drag is realized, in which
the hydrodynamic velocities in both layers become equal in the interior of the
systems. Estimates are given for the monolayer and bilayer graphene devices.
The predictions of our theory can be tested by the high-resolution thermal
imaging and Johnson-Nyquist nonlocal noise thermometry.
