  We examine the problem of state transformations in the framework of Gaussian
thermal resource theory in the presence of catalysts. To this end, we introduce
an expedient parametrisation of covariance matrices in terms of principal mode
temperatures and asymmetries, and consider both weak and strong catalytic
scenarios. We show that strong catalysts (where final correlations with the
system are forbidden) are useless for the single mode case, in that they do not
expand the set of states reachable from a given initial state through Gaussian
thermal operations. We then go on to prove that weak catalysts (where final
correlations with the system are allowed) are instead capable of reaching more
final system states, and determine exact conditions for state transformations
of a single-mode in their presence. Next, we derive necessary conditions for
Gaussian thermal state transformations holding for any number of modes, for
strong catalysts and approximate transformations, and for weak catalysts with
and without the addition of a thermal bath. We discuss the implications of
these results for devices operating with Gaussian elements.
