  Thin film YIG (Y$_3$Fe$_5$O$_{12}$) is a prototypical material for
experiments on thermally generated pure spin currents and the spin Seebeck
effect. The 3-omega method is an established technique to measure the
cross-plane thermal conductance of thin films, but can not be used in YIG/GGG
(Ga$_3$Gd$_5$O$_{12}$) systems in its standard form. We use two-dimensional
modeling of heat transport and introduce a technique based on Bayesian
statistics to evaluate measurement data taken from the 3-omega method. Our
analysis method allows us to study materials systems that have not been
accessible with the conventionally used 3-omega analysis. Temperature dependent
thermal conductance data of thin film YIG are of major importance for
experiments in the field of spin-caloritronics. Here we show data between room
temperature and 10 K for films covering a wide thickness range as well as the
magnetic field effect on the thermal conductance between 10 K and 50 K.
