This paper has experimentally addressed the determination of the convection coefficient for a nichrome and nickel-titanium (NiTi) shape memory alloy (SMA) wire subjected to constant load, heated by electrical current and cooled by free convection (with the current switched off). The entire cycle of actuation is such that the temperature field is allowed to reach a steady state during heating, and the ambient temperature during cooling. The experiments, in conjunction with a phenomenological model, suggest that the convection coefficient can be represented as h = a 0 + a 1 I , where I is the electric current in the wire. The parameter h is highly sensitive to the material (nichrome or SMA) through the zeroth-order coefficient (a 0 ) whereas it is weakly sensitive to I (or the strength of the heat source) through the first-order coefficient (a 1 ). Further, for a given material, h (through a 0 ) is strongly dependent on whether the wire is being heated or cooled. This is in contrast with the customary practice in the literature where h is taken to be identical for heating and cooling. Finally, a simple empirical model in terms of a convection-like parameter, α, is also tested (with a view towards control applications) and is found to be highly accurate in simulating the experimental results.