Abstract In order to explain proton spin-lattice relaxation measurements in a deuterated copper Tutton salt , we performed a theoretical investigation of the thermal contact between the proton Zeeman system (PZS) and the electron dipole-dipole interaction system (EDDS). The basic process that maintains the contact between these two spin systems is a three-spin process in which one proton spin and two electron spins make a simultaneous transition. We calculated the transition probability of this three-spin process. It was proved that neither electron spin-lattice relaxation nor cross-relaxation are a bottle-neck in the proton spin-lattice relaxation, so the observed relaxation time values are completely determined by this three-spin process. Hence, the contact time between the PZS and the EDDS can be derived directly from the measurements.