Among potential energy storage solutions, many require the development of major infrastructures (hydraulics sites, subterranean cavities, hydrogen storage systems). That is why, more recently, the carbon-free electricity storage into synthetic fuels is of increasing interest, representing an alternative with great potential called "Power to gas ". The manufacture of a synthetic fuel from water, carbon dioxide and carbon-free electricity meets a number of objectives for overall efficiency improvement: - Reducing CO2 emissions from fossil fuel use, - offering CO2 reuse rather than storing it for an indefinite period, - Turning all carbon-free electrical sources (renewable and nuclear), especially during periods of overproduction into a storable product, with the possibly of regenerating electricity during periods of production deficits. In this perspective of reducing CO2 emissions, High Temperature Steam Electrolysis (HTSE) is a promising way to produce massively hydrogen. This process operates at high temperatures (> 700 ° C). The operating conditions with vapor and high temperature reduce the amount of consumed electrical energy by the electrolysis reaction. This has to be realized by increasing the thermal energy part, coming from cheap sources. In addition, this high temperature based technology allows either solid oxide electrolysis of H2O steam to produce H2 and / or co-electrolysis of H2O + CO2 which produces syngas (H2 + CO), paving the way for the production of hydrocarbons including methane. Producing synthetic natural gas then gives the possibility of using immediately all existing infrastructures: transmission and distribution, storage capacity, power generation facilities, etc ... This technology offers very high performance by lowering the amount of electricity required, provided high level of heat recovery, especially to vaporize the water. Here are presented schemes involving several processes with high temperature electrolysis or co-electrolysis technology coupled with a catalytic CO2 or CO hydrogenation reactor. This type of reactors is highly exothermic. Therefore a thermal integration is proposed but an external heat source should also be added, modifying the process schemes. For a power and a level of available heat source temperature, the several schemes to produce methane are therefore optimized and compared according to their efficiencies, produced methane quality, heat recovery and recycled CO2 amount. Moreover for both electrolysis and co-electrolysis, this work provides real operating points for the electrolysis step [1-2], such as voltage, current, possible steam conversion, gas composition, pressure level …etc. The considered catalytic reactor is a Gibbs one. It is shown that in case of low available external heat power, the co-electrolysis mode can offer the best efficiency. Moreover, the co-electrolysis Area Specific Resistance (ASR) is found experimentally close to the steam electrolysis one, leading to a limited impact on the required electrochemical surface. These results confirm the potential of this technology to store the carbon-free electricity: very high efficiencies thanks to the high temperature operation and a very promising help to recycle the CO2 into synthetic fuels. [1] J. Laurencin et al., 2011, Journal of Power Sources, 196, 2080-2093.[2] J. Aicart et al, 2014, Fuel Cells, Vol.14, 3, 430-447 Figure 1