It is a known result in the literature that a one-dimensional chain of particles that interact harmonically with its first neighbors does not conduct heat, and nonlinear forces are needed to reproduce Fourier's law of heat conduction. When asymmetries are introduced in such a conducting system, a rectifying effect is obtained where the thermal current shows different magnitudes depending on which side of the chain has higher temperature, such devices being called thermal diodes. In this work we study both phenomena, heat conduction and thermal rectification, in a onedimensional chain of particles, with fixed boundary conditions, coupled to two thermal baths, one at each end, modeled as Langevin thermostats.The particles interact with their first neighbors harmonically and have a nonlinear on-site potential, for which we study two types, Frenkel-Kontorova and φ 4 potentials. We verify that, for both cases, Fourier's law is observed, where the temperature profile and the thermal conductivity are dependent on the relation between the harmonic and anharmonic amplitudes, and the system's average temperature. Next, to create an asymmetry in the chain, we coupled two different segments of equal lengths. We observed a rectifying effect, where the preferential direction differs for each of the two on-site potentials studied. How the heat-bath temperatures changes the magnitude of rectification was also observed. We also investigated the effect of interfacial nonlinearities through a power-law potential, coupling φ 4 segments. By changing the power-law exponent, we looked for the conditions under which optimal rectification is achieved.