Methods to determine the thermal conductivity of liquids have come under increased scrutiny recently due to their relative importance in determining the precise physical mechanisms responsible for heat flow in different materials and at multiple length scales. In transient-based systems, one important but often overlooked parameter is the onset of natural convection. In the first part of this study, the transient effects of natural convection are analyzed numerically for a relatively new transient thermal characterization system (transient hot disk) in order to determine when they begin to affect the calculation of a surrounding fluid's thermal conductivity. A comprehensive analysis of the effect of a fluid's pertinent thermophysical properties, Rayleigh number and Prandtl number on the sensor temperature response during testing is completed. Subsequently, a correlation is developed to determine the onset of natural convection during testing for fluids having a wide range of Prandtl numbers. The solution is verified using experimentation with multiple fluids having known, temperature-dependent volumetric heat capacities. The correlation is used as part of a new method to accurately calculate the thermal conductivity of different Newtonian fluids in Part II of this study, which is published separately. (C) 2013 Elsevier Ltd. All rights reserved.