Apparatus suitable for the thermal conversion of methane to hydrocarbons of higher molecular weight, comprising an elongated reactor 1 provided with an inlet 5 for supplying a gas mixture containing methane (process gas) and an outlet at the opposite end, the reactor over a first part towards the inlet end having a plurality of electric heaters 3 surrounded by sheaths 4. The heaters, e.g., electric resistors, which are spaced apart and are substantially parallel with respect to one another, are arranged in substantially parallel rows perpendicular to the axis of the reactor so as to permit circulation of the process gas and/or effluent between the sheaths and/or between the sheaths and walls 22 separating two consecutive rows. The heaters heat the passages by successive independent cross sections substantially perpendicular to the axis of the reaction. Towards the outlet end, the reactor further comprises an injector for supplying cooling fluid, which cools the effluent. The reactor also has a hydrogen inlet for introducing a gas containing hydrogen into the space surrounding the heaters inside the sheaths 4 at an appropriate pressure. The reactor and the sheaths 4 are designed so that hydrogen is diffused from inside the sheaths to outside them and can then be diluted in the process gas.