Thermally induced spin transitions in a family of heterospin polymer chain complexes of Cu2+ hexafluoroacetylacetonate with two pyrazole-substituted nitronyl nitroxides are studied using electron paramagnetic resonance (EPR) spectroscopy. The structural rearrangements at low temperatures induce spin transitions in exchange-coupled spin triads of nitroxide-copper(II)-nitroxide. The values of exchange interactions in spin triads of studied systems are typically on the order of tens to hundreds of inverse centimeters. The large magnitude of exchange interaction determines the specific and very informative peculiarities in EPR spectra due to the predominant population of the ground state of a spin triad and spin exchange processes. The variety of these manifestations depending on structure and magnetic properties of spin triads are described. EPR is demonstrated as an efficient tool for the characterization of spin transitions and for obtaining information on the temperature-dependent sign and value of the exchange interaction in strongly coupled spin triads.