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The strain effect on critical current (Ic( Delta *e)) in Y Ba2Cu3O7 - Delta *d (YBCO) coated conductors was evaluated at temperatures in the range 20--83 K under magnetic fields parallel to the c-axis up to 10 T. The peaked reversible variation of Ic with applied uniaxial strain was confirmed in the self-field at all tested temperatures. The strain sensitivity increases with increasing temperature, resulting in a more pronounced reversible suppression with strain at higher temperature. Interestingly, it was found that the peak strain corresponding to the maximum of Ic shifts to the compressive side with decreasing temperature. Such a peak shift cannot be explained by a change in the thermal residual strain of the YBCO film, suggesting that the peak strain of the Ic( Delta *e) in YBCO coated conductors is not determined only by relaxation of the residual strain. The strain sensitivity of Ic( Delta *e) at 60 K becomes greater with increasing magnetic field, while the influence of the magnetic field is much less pronounced at 20 K. The in-field Ic( Delta *e), including the compressive strain region as well as the tensile region, shows a double peak behavior at low magnetic field at 77 and 83 K. The temperature and magnetic field effect on Ic( Delta *e) in YBCO coated conductors is discussed considering flux pinning within the grains and on grain boundaries.