We have measured the heat capacity of 3He adsorbed on three-dimensionally connected nanopores, 2.7 nm in diameter, preplated with about 1.3 atomic layers of 4He. At low coverages of 3He, the 3He heat capacity is roughly constant at the measured temperatures between 0.1 and 1 K. Its molar heat capacity is on the order of the gas constant R, between 1.1R and 1.8R. This suggests a Boltzmann gas state of the adsorbed 3He. At high coverages, the heat capacity is likely approaching linear in T at low temperatures, which suggests a degenerate state at further lower temperatures.