  Substitution of Sb in FeSb$_2$ by less than 0.5% of Te induces a transition
from a correlated semiconductor to an unconventional metal with large effective
charge carrier mass $m^*$. Spanning the entire range of the semiconductor-metal
crossover, we observed an almost constant enhancement of the measured
thermopower compared to that estimated by the classical theory of electron
diffusion. Using the latter for a quantitative description one has to employ an
enhancement factor of 10-30. Our observations point to the importance of
electron-electron correlations in the thermal transport of FeSb$_2$, and
suggest a route to design thermoelectric materials for cryogenic applications.
