In the overwhelming majority of the exchange-coupled clusters investigated in field of molecular magnetism, the exchange interaction is constant on temperature. ''Breathing'' crystals of composition Cu(hfac)(2)L-R undergo temperature-induced reversible structural rearrangements accompanied by significant changes of the effective magnetic moment. Using high-field (W-band) EPR, we provide a solid proof of drastic temperature dependence of exchange interaction J(T) in these compounds that originates from temperature dependence of inter-spin distances. Strong dependence J(T) revealed by EPR makes Cu(hfac)(2)L-R breathing crystals interesting and promising systems in the research toward creation of molecular-magnetic switches and related spin devices.