A phase change for the condensed matter comprising large nuclei is proposed as a heat sink during an episode of accelerated nuclear decay, being particularly relevant to the formation of radiohalos. The proposed nuclear phase change would occur in 206Pb nuclei, being the final stable progeny in the 238U decay chain. With each cascade of decays, the latent heat for this presumed first order phase transition would be taken from (via heat transfer, generically invoked), and thereby continuously cool, the radio-center's immediate environment wherein the thermal energy is deposited. Arguing by analogy with atomic/molecular systems, the plausibility of providing sufficient cooling (absorbing enough energy) by a phase change is explored. The lower entropy phase for large, unstable nuclei during accelerated decay might consist of alpha clusters as compared with primarily nucleon pairings for the normal phase. The nuclear phase change would occur with/at the switch from unstable parent isotope to stable daughter in accordance with the dependence of a hypothetical nuclear phase diagram on the decreased strength of the nuclear force (a shallower nuclear potential) for unstable nuclei characterizing an episode of accelerated decay as compared with normalcy, as will be explained in—Part II.