The onset of thermomagnetic convection in ferrofluid in a vertical transient hot-wire cell is analytically and experimentally investigated by studying the temperature rise of an electrically-heated wire. During the initial stage of heating, the temperature rise is found to correspond well to that predicted by conduction only. For high electrical current densities, the initial heating stage is followed by a sudden change in the slope of the temperature rise with respect to time as a result of the onset of thermomagnetic convection cooling. The observed onset of thermomagnetic convection was then compared to that of natural convection of deionized water. For the first time, the critical time corresponding to the onset of thermomagnetic convection around an electrically-heated wire is characterized and non-dimensionalized as a critical Fourier number (Foc). We propose an equation for Foc as a function of a magnetic Rayleigh number to predict the time for the onset of thermomagnetic convection. We observed that thermomagnetic convection in ferrofluid occurs earlier than natural convection in non-magnetic fluids for similar experimental conditions. The onset of thermomagnetic convection is dependent on the current supplied to the wire. The findings have important implications for cooling of high-power electronics using ferrofluids and for measuring thermal properties of ferrofluids.