Ti-51Ni(at%) and Ti-40Ni-10Cu(at%) alloy wires with diameters of 0.3mm, 0.5mm and 0.7mm were prepared by drawing the alloy ingots fabricated by vacuum induction melting. Heating rates of the wires were investigated by measuring changes in temperatures of them while applying currents in the range of 1 A and 6 A to them and cooling rates were investigated by measuring changes in temperatures of them after cutting currents. Heating rate increased with increasing the amount of current, while cooling rate was kept constant. Both heating rate and cooling rate increased with decreasing diameter of wire. This suggested that high amount of current and small wire diameter were required for high heating and cooling rate. Comparing Ti-50Ni alloy wires with Ti-40Ni-10Cu alloy wires, heating rates of the latter was faster than that of the former, although cooling rates were almost same. This suggested that Ti-40Ni-10Cu alloy wires is better than Ti-50Ni alloy wires for the applications requiring high actuating rates.