The effect of the strength of the self-induced magnetic field around a current carrying wire on thermomagnetic convection cooling in ferrofluid is experimentally and numerically investigated. Temperature-rise characteristics of the hot micro-wire for uniform Joule heating with different electric currents are compared to identify the relative importance of the strength of the axisymmetric magnetic field. Experiments are done with copper and platinum wires with current inputs adjusted to achieve the same Joule heating per unit length of wire. It was found that at high current supply (2A), mixing in ferrofluid is escalated due to thermomagnetic convection that resulted into 28% increase in average Nusselt number value which finally resulted into temperature drop of 8 K in comparison to DIW. Comparison of results for different self-induced magnetic field strengths in ferrofluid and deionized water clearly show that the observed cooling phenomenon is due to the self-induced magnetic field interacting with the magnetic fluid rather than natural-convection or other nanofluid-related mechanisms. For 1.83 W J heating, the temperature of the copper wire is 6 K lower than that of the platinum wire. Temperature and velocity contours obtained from simulations based on a 2-D single-phase model including a temperature-dependent magnetic body force provide flow visualization and further confirmed that the thermomagnetic cooling is responsible for the observed behaviour.