Performance of an innovative storage system for renewable energy, based on the Power-to-Gas concept are numerically predicted. The investigated system is composed by a high temperature co-electrolyzer of Solid Oxide Electrolyte Cell technology and an experimental methanation section, based on structured catalyst, suitable for high temperature operation. With the aim to thermally integrate high temperature co-electrolysis and methanation, a parametric thermodynamic analysis of the Power-to-Gas system is carried-out with a lumped-parameters approach, including all the thermal and electric energy consumptions. In particular, in order to optimize the system thermal balance of plant, various configurations involving internal heat recovery and pressurization of components are also considered. Numerical results are provided in terms of different performance indicators, such as electric-to-fuel conversion index, first law efficiency and second law efficiency and output-fuel quality indicators. The study demonstrates the possibility to thermally integrate the co-electrolyzer and the high-temperature methanation section achieving significant energy savings. Moreover, the calculated results show that the system set-up providing higher quality of the produced synthetic natural gas do not always lead to larger values in energy conversion efficiency. Eventually, advanced configurations of the Power-to-Gas system including heat recovery allow to achieve first-law efficiency up to values around 80-85% and second-law efficiency around 70-78%; a second methanation section based on conventional low-temperature reactors is included in the system and pressurization of the methanation section, or pressurization of the co-electrolysis section, is mandatory, in order to achieve large fraction of methane (up to 95-99%) in the produced synthetic fuel.