The ferroelectric degenerate semiconductor Sn$_{1-delta}$Te exhibits superconductivity with critical temperatures, $T_c$, of up to 0.3 K for hole densities of order 10$^{21}$ cm$^{-3}$. When doped on the tin site with greater than $x_c$ $= 1.7(3)%$ i
ndium atoms, however, superconductivity is observed up to 2 K, though the carrier density does not change significantly. We present specific heat data showing that a stronger pairing interaction is present for $x > x_c$ than for $x < x_c$. By examining the effect of In dopant atoms on both $T_c$ and the temperature of the ferroelectric structural phase transition, $T_{SPT}$, we show that phonon modes related to this transition are not responsible for this $T_c$ enhancement, and discuss a plausible candidate based on the unique properties of the indium impurities.
