We present a comprehensive series of electrical transport (conductivity, magnetoresistance, and Hall effect), thermodynamic (specific heat, magnetic susceptibility, and magnetization), and optical (reflectivity) measurements in varying temperature ranges between 0.05 and 330 K on high-quality FeSi single crystals grown by vapor transport. The entire set of data can consistently be described with the usual relations for a (compensated $n$ type) semiconductor if an unconventional band structure is assumed. Compared to the results of mean-field band-structure calculations, the height of the peaks in the total density of states around the energy gap is considerably enhanced, implying enhanced effective masses. Most likely correlation effects are the source of these features. At very low temperatures we encounter metallic behavior. A low concentration of correlated itinerant charge carriers coexists with interacting magnetic moments.