Following experiments performed with deuterided high-temperature superconductors (HTSCs) at the underground Gran Sasso Laboratory, the capacity of these materials to absorb deuterium and the role played by nonequilibrium conditions in neutron burst emissions in the framework of cold fusion have been determined. Taking into account that HTSC materials such as Y1Ba2Cu3O7-δ (YBCO) are able to absorb deuterium without destroying the crystalline structure, deuterated YBCO pellets were placed in a neutron radiation field, and thermal cycles were operated. In this double nonequilibrium condition, neutron rate enhancement was sought by selecting “time-correlated” burst-like events. The pellets and high-pressure D2 gas were enclosed in a stainless steel vessel, and thermal cycles (300 to 77 to 300 K) were performed; moreover, for comparison, background and blank runs were performed. A specific acquisition system, able to detect multiple neutron signals in defined time windows, was set up. One thermal cycle run showed a large increase (seven times more, corresponding to >30 standard deviations) of time-correlated events with respect to the blanks. In another run, although no relevant mean value increase in events was detected, one interesting multiple (triple) neutron signal occurred at a temperature (∼95 K) close to the transition from superconducting to the normal state. These multiple events were sporadic (detected twice during four thermal cycles lasting ∼3 h), although the probability that these events were simulated by the background was quite low (one incident expected in 80 h). Similar runs produced no relevant values. Another experiment, at constant temperature (300 K), characterized by a heavy D2 gas refill, showed both some increase in time-correlated events and a few triple neutron signals.