To develop next-generation electronics and high efficiency energy-harvesting devices, it is crucial to understand how charge and heat are transported at the nanoscale. Metallic atomic-size contacts are ideal systems to probe the quantum limits of transport. The thermal conductance and electrical conductance of gold atomic contacts have been recently proven to be quantized at room temperature. However, a big experimental challenge in such measurements is represented by the fast breaking dynamics of metallic junctions at room temperature, which can exceed the typical response time of the thermal measurement. Here, we use a break-junction setup that combines Scanning Tunneling Microscopy with suspended microelectro-mechanical systems with a gold-covered membrane and an integrated heater acting also as a thermometer. By using other metals as tip materials, namely, Pt, PtIr, and W, we show heat transport measurements through single gold atomic contacts. The dependence of the thermal conductance is analysed as a function of contact size and materials used. We find that by using Pt and Pt-Ir tips, we can maximize the mechanical stability and probability of forming single Au atomic contacts. We then show the quantization of the electrical and thermal conductance with the verification of the Wiedemann-Franz law at the atomic scale. We expect these findings to increase the flexibility of experimental techniques probing heat transport in metallic quantum point contacts and to enable the investigation of thermal properties of molecular junctions.