Using the full many-body spectrum of the two-dimensional infinite-U Hubbard model obtained by exact diagonalization, we study transport and thermodynamic properties across a wide range of temperatures. We identify a crossover scale T_{quant} \lesssim t, below which the system departs from a high-temperature strongly correlated classical fluid and enters a regime in which quantum effects become strong while transport remains highly incoherent. We argue that this defines an intermediate semi-quantum regime, distinct from both the classical fluid at higher temperatures and the coherent quantum fluid that emerges only at much lower temperatures. In this regime, at temperature scales relevant to the normal state of correlated materials such as the cuprates, the resistivity exhibits persistent T-linear bad-metal behavior, exceeding the Mott-Ioffe-Regel limit without a sharp transport crossover. By contrast, thermodynamic observables such as the compressibility display a clear crossover, directly revealing the onset of semi-quantum behavior. We propose the semi-quantum regime as a useful framework for understanding transport in strongly correlated electron fluids.