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We investigate the fluctuations of the diquark-pair field and their effectson observables above the critical temperature $T_c$ in two-flavor colorsuperconductivity (CSC) at moderate density using a Nambu-Jona-Lasinio-typeeffective model of QCD. Because of the strong-coupling nature of the dynamics,the fluctuations of the pair field develop a collective mode, which has aprominent strength even well above T_c. We show that the collective mode isactually the soft mode of CSC. We examine the effects of the pair fluctuationson the specific heat and the quark spectrum for T above but close to T_c. Wefind that the specific heat exhibits singular behavior because of the pairfluctuations, in accordance with the general theory of second-order phasetransitions. The quarks display a typical non-Fermi liquid behavior, owing tothe coupling with the soft mode, leading to a pseudo-gap in the density ofstates of the quarks in the vicinity of the critical point. Some experimentalimplications of the precursory phenomena are also discussed.Comment: 39 pages, 26 eps figures. The published version to appear in Prog.  Theor. Phys. 114 (2005), 117-155. The references are up-date

Pre-Critical Phenomena of Two-Flavor Color Superconductivity in Heated Quark Matter: -- Diquark-Pair Fluctuations and Non-Fermi Liquid Behavior --