Shock temperature and melting temperature measurements are of importance to construct complete equation-of-states of materials. In this article, we overviewed the one-dimensional heat conduction model at ideal interface and model at non-ideal interface in Hugoniot temperature measurements of metals, focusing on the reasonability or tenability of the inclusive and implicative assumptions in models, and the principal factors influencing the resultant temperature. The discussed issues deal with the assumptions of the heat conductivity at shock compression independent of temperature to derive an analytical solution to the interface temperature, that of the greybody emitter of the sample/window interface at shock compression, the transparency of window under shock temperature, the correction of apparent interface temperature to ideal interface temperature in non-ideal interface model, the measurements for melting temperature under shock compression, and the non-Flourier heat conduction at the interface. The investigations show that the metal-sample/window interfacial radiation measurements can yield an approximate Hugoniot temperature, and even an approximate melting temperature at interface pressure in the case of melting as a whole.