An incomplete thermal cycle upon heating of a shape memory alloy (arrested at a temperature between austenite transformation start and finish temperatures, As and Af) induced a kinetic stop in the next complete thermal cycle. The kinetic stop temperature was closely related to the previous arrested temperature. This phenomenon is named temperature memory effect (TME). In this work, the TME induced by incomplete cycling in TiNi and TiNiCu ribbons, TiNiCu thin films and TiNiCu wire showing two-way shape memory effect was systematically investigated by performing either a single incomplete cycle, or a sequence of incomplete cycles with different arrested temperatures. Results showed that the TME is a common phenomenon in shape memory alloys, caused by a partial martensite to parent phase (M → P) transformation. N points of temperatures could be memorized if N times of incomplete cycles on heating were performed with different arrested temperatures in a decreasing order. On the contrary, if a partial parent phase to martensite (P → M) transformation was performed by an incomplete cycle on cooling, the next complete P → M transformation did show any evidence of TME. The incomplete cycle of parent phase to R-phase and R-phase to parent phase transformations did not show any evidence of TME. Results showed that the capability to memorize the temperature is a specific characteristic of the martensitic phase, and the decrease in microstrains and elastic energy after ICH procedure has significant contributions to the TME.