Abstract: The thermal control device comprises at least one network of capillary heat pipes, in which each heat pipe comprises a tube enclosing an essentially annular longitudinal capillary structure, for the circulation of a two-phase heat-transfer fluid in the liquid phase, and surrounding a central channel for the circulation of said two-phase fluid in the vapor phase. The tubes of at least two heat pipes of the network intersect and are interconnected in such a way that at each intersection of heat pipes forming a node of the network, an exchange of fluid in the liquid phase can take place by capillary action between the capillary structures of said two or more heat pipes, and such that, simultaneously, an exchange of fluid in the vapor phase can take place by free circulation between the central channels of said two or more heat pipes.