For a TTHE-A and parallel flow of the refrigerant medium (fluids 0 and 2 ) and hot fluid (fluid 1), for 𝑄 𝑣𝑜 ≫ 𝑄 𝑣2 , Batmaz and Sandeep observed the occurrence of a point 𝑥 = CP in which 𝑇 1 = 𝑇 2 , and 𝑇 2 is maximum. They called CP the Crossover Point. Also, for TTHE-A, when 𝑄 𝑣0 ≪ 𝑄 𝑣2 , Bertoli et al. demonstrated the possibility of CP (1,0) , i.e., crossover point between fluids 1 and 0. For TTHE-A, explicit expressions for the occurrence conditions of CP (1,0) and CP and their location were presented by Bertoli et al. . Also, in counter-current flow the effectiveness of TTHEs is greater than that of equivalent DTHEs, but in the case of co-current flow with CP this may not be true . This parameter is, therefore, clearly of interest in the design of TTHEs. However, there is limited knowledge about CP for TTHE-HL. Thus, in the following analysis, approximate expressions are developed to locate the dimensionless residence time for temperature equality between streams 1 and 2, 𝜏é 𝑝 , and between streams 1 and 0, 𝜏é 𝑝(1,0) . Following Batmaz and Sandeep , if 𝜏é 𝑝(𝑚,𝑛) is also maximum for the cold stream temperature, then we call it CP.