  The relaxation of a system to a steady state is a central point of interest
in many attempts to advance control over the quantum world. In this paper, we
consider control through instantaneous Gaussian unitary operations on the
ubiquitous lossy channel, and find locally optimal conditions for the cooling
and heating of a multimode Gaussian state subject to losses and possibly
thermal noise. This is done by isolating the parameters that encode entropy and
temperature and by deriving an equation for their evolution. This equation is
in such a form that it grants clear insight into how relaxation may be helped
by instantaneous quantum control. It is thus shown that squeezing is a crucial
element in optimising the rate of change of entropic properties under these
channels. Exact relaxation times for heating and cooling are derived, up to an
arbitrarily small distance from the fixed point of the lossy channel with
locally optimal strategies.
