If the reverse transformation of a shape memory alloy is arrested, a kinetic stop will appear in the next complete transformation. The kinetic stop temperature has a close relation with the previous arrest temperature. This kinetic stop can be regarded as a "memory" of the previous arrest temperature. This phenomenon is named temperature memory effect(TME). The TME induced by incomplete cycling in Ti-Ni-Nb and Ti-Ni-Cu alloys was systematically investigated by performing either a single incomplete cycle, or a sequence of incomplete cycles with different arrested temperatures. The results indicate that TME only exists in the heating process, and TME can occur both in B19→B2 and B19→B2 reverse transformation during heating process. But, there is no evidence of TME during cooling in the Ti-Ni-X ternary alloys. And the reverse transformation temperature interval (Af-As) of the Ti44-Ni47-Nb9 alloy induced by TME can be significantly enlarged compared with that of the Ti-Ni-Cu alloy by performing multi-times incomplete transformation cycling with a decreasing order arrested temperature.