The temperature dependence of the conductance of a quantum point contact has been measured. The conductance as a function of the Fermi energy shows temperature-independent fixed points, located at roughly multiple integers of e(2)/h. Around the first fixed point at e(2)/h, the experimental data for different temperatures can be scaled onto a single curve. For pure thermal smearing of the conductance steps, a scaling parameter of one is expected. The measured scaling parameter, however, is significantly larger than 1. The deviations are interpreted as a signature of the potential landscape of the quantum point contact, and of the source-drain bias voltage. We relate our results phenomenologically to the metal-insulator transition in two dimensions.