Low-temperature thermodynamic properties of strongly interacting Fermi liquids with a fermion condensate are investigated. We demonstrate that the spin susceptibility of these systems exhibits the Curie-Weiss law, and the entropy contains a temperature-independent term. The excessive entropy is released at the superconducting transition, enhancing the specific heat jump deltaC and rendering it proportional to the effective Curie constant. The theoretical results are favorably compared with the experimental data on the heavy-fermion metal CeCoIn5, as well as 3He films.