The measurement of the thermal conductivity of liquids is rather complicated due to the nature of the fluid. To the conduction, which has to be characterized, are added the natural convection, the radiative transfer, and the perturbations caused by the presence of enclosure walls. The goal of this work, composed of two parts, is to implement an experimental bench allowing the measurement of the thermal diffusivity and thermal conductivity of liquids. The first part (Part I) presented here, is about pure conduction and focuses on several aspects involved in this measurement, which will lead one, based on theoretical and practical considerations, to choose a pulse method in a one-dimensional (1D) and cylindrical geometry to solve the problem. In the second section of this part, the problem of the parameters estimation is investigated with the presence of the walls of the measuring cell and this will allow us to define the characteristics of the walls (thickness and thermophysical properties). The entire problem is treated through the thermal quadrupoles method. Finally, in a last section, a setup at room temperature is described. The second part (Part II) of this work that is presented in another paper will show how it is possible to get rid of the convection by a judicious choice of the extension of the measuring cell and how the radiation effects can be taken into account to perform measurements at high temperatures (up to 500°C).