Heat treatments are inevitable not only in the production of rare earth barium copper oxide (REBCO) tapes, but also in their post-processing for applications, typically, in soldering and epoxy/wax impregnation during the fabrication of REBCO coils. In general, the heat treatment of REBCO tapes should be carried out at lower temperature for a shorter time, but the specific safe boundary of heat-treatment temperature and time for REBCO tapes is still unknown. Therefore, a comprehensive study on the typical electrical, mechanical, and electromechanical characteristics of REBCO tapes after heat treatments under temperature of 250 ℃ is necessary. This work focus on the copper-encapsulated REBCO tapes, which are more robust (while with much lower engineering current density) to be processed in application systems than the tapes without encapsulation. The critical current degradation, stress-strain characteristic, and electromechanical properties of REBCO tapes were measured after heat treatments at different temperatures in argon and oxygen atmosphere. A 2D finite element analysis model was established for detailed stress/train analyzes under tension and bending based on the analysis of residual stress/strain. The results indicate that the critical current of the copper-encapsulated REBCO tapes decreases with increasing heat-treatment temperature and dwell time, and is of no evident relation to atmosphere. In addition, increased temperature of heat treatment leads to an obvious decrease in the yield strength and critical tensile stress. This effect is mainly attributed to the degradation of mechanical properties of the encapsulated copper layer, which is demonstrated by the combination of our finite element simulation and the experiments results. Interestingly, the change in the critical bending radius due to heat treatments was slight, because the bending axial strain of the REBCO layer remained almost unchanged after heating. It is also worthy to note that all the properties tested in this study were irrelevant to the external oxygen partial pressure during the heating process. As a practical conclusion for the application systems, an upper and atmosphere-irrelevant limit of processing temperature of 130 or 150 ℃ (2 h dwell time) was proposed for copper-encapsulated REBCO tapes, under which the critical current, yield strength, critical tensile stress/strain and critical bending radius of the copper-encapsulated REBCO tapes decay by < 1% or 3%, respectively.