We consider a system consisting of two interacting classical particles, each one subject to an on-site potential and to a Langevin thermal bath. We analytically calculate the heat current that can be established through the system when the bath temperatures are different, for weak nonlinear forces. We explore the conditions under which the diode effect emerges when inverting the temperature difference. Despite the simplicity of this two-particle diode, an intricate dependence on the system parameters is put in evidence. Moreover, behaviors reported for long chains of particles can be extracted, for instance, the dependence of the flux with the interfacial stiffness and type of forces present, as well as the dependencies on the temperature required for rectification. These analytical results can be a tool to foresee the distinct role that diverse types of nonlinearity and asymmetry play in thermal conduction and rectification.