Following the idea of nucleon clustering and light-nuclei production in relativistic heavy-ion collisions close to the QCD critical-end point, we address the quantum effects affecting the interaction of several nucleons at finite temperature. For this aim we use the $K$-harmonics method to four-nucleon states ($alpha$ particle), and also develop a novel semiclassical flucton method at finite temperature, based on certain classical paths in Euclidean time, and apply it to two- and four-particle configurations. To study possible effects on the light-nuclei production close to the QCD critical point, we also made such calculations with modified internuclear potentials. For heavy-ion experiments, we propose new measurements of light-nuclei multiplicity ratios which may show enhancements due to baryon preclustering. We point out the special role of the $mathcal{O}(50)$ four-nucleon excitations of $alpha$-particle, feeding into the final multiplicities of $d,t$, $^3$He and $^4$He, and propose to directly look for their two-body decays.
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