In this paper we describe an experimental setup designed to measure simultaneously and very accurately the resistivity and the absolute thermoelectric power, also called absolute thermopower or absolute Seebeck coefficient, of solid and liquid conductors/semiconductors over a wide range of temperatures (room temperature to 1600 K in present work). A careful analysis of the existing experimental data allowed us to extend the absolute thermoelectric power scale of platinum to the range 0-1800 K with two new polynomial expressions. The experimental device is controlled by a LabView program. A detailed description of the accurate dynamic measurement methodology is given in this paper. We measure the absolute thermoelectric power and the electrical resistivity and deduce with a good accuracy the thermal conductivity using the relations between the three electronic transport coefficients, going beyond the classical Wiedemann-Franz law. We use this experimental setup and methodology to give new very accurate results for pure copper, platinum, and nickel especially at very high temperatures. But resistivity and absolute thermopower measurement can be more than an objective in itself. Resistivity characterizes the bulk of a material while absolute thermoelectric power characterizes the material at the point where the electrical contact is established with a couple of metallic elements (forming a thermocouple). In a forthcoming paper we will show that the measurement of resistivity and absolute thermoelectric power characterizes advantageously the (change of) phase, probably as well as DSC (if not better), since the change of phases can be easily followed during several hours/days at constant temperature.