We report on the sensitivity of superconducting transition temperature (Tc) to the individual layers' thickness in Mo/Au proximity bilayers to be used in Transition-Edge Sensors. The achieved good reproducibility and quality of the bilayers allow a clear determination of the superconducting critical temperature Tc as a function of the Mo and Au thicknesses. One objective of this work is to analyse the quality of the Mo-Au interface and to assess the possible effects of the double Au layer we use to fabricate these bilayers and TESs based on them. Experimental data are analysed on the base of Usadel equations using the model developed by Martinis and co-workers, in which the proximity effect in the bilayer is mainly governed by the interface transparency between the superconductor and the normal metal. We find that this model describes quite well the behaviour of Tc, even for quite thick Au layers, and that the double Au layer does not play any relevant role on the proximity effect.