We present experimental data of the temperature-dependent subharmonic energy-gap structure (SGS) in the current-voltage (I-V) curves of superconducting niobium point contacts. The observed SGS is modified by heating effects. We construct a model of the quasiparticle conductance of metallic superconducting weak links that includes the heating effects self-consistently. Our model is combined with that of Octavio, Blonder, Klapwijk, and Tinkham [Phys. Rev. B 27, 6739 (1983)], which is based on the idea of multiple Andreev scattering in the contact. The shape and the temperature variation of the calculated SGS is found to be in good agreement with the experimental curves for contacts with resistance larger than 5 Ω.