We conducted experiments to study the stability of a ferrofluid cylinder in an azimuthal magnetic field. The ferrofluid cylinder is formed on a current-carrying wire for creating the azimuthal magnetic field and is surrounded by a non-magnetic fluid of the same density to neglect the gravitational effect. Experiments were performed for different wire and cylinder radii. Data were analyzed to extract the growth rate and the wavelength of the perturbation characterizing the ferrofluid cylinder. The influence of the wire radius on the cylinder stability is used to respond to an issue, recently raised, in relation to the growth rate data obtained by the first experimental work. The results of the experiments confirm the theoretical predictions, namely, a decrease in the growth rate when the ratio between the wire radius and the ferrofluid cylinder radius increases. However, the isothermal theory overpredicts the growth rate observed in this experiment and sources of this discrepancy are explored. In particular, a theoretical model considering a thermocapillary effect is developed and it is shown that this non-isothermal theory can explain the observed discrepancy.