  The temperature dependence of the London penetration depth $\Delta\lambda(T)$
in the superconducting doped topological crystalline insulator
Sn$_{1-x}$In$_x$Te was measured down to 450 mK for two different doping levels,
x $\approx$ 0.45 (optimally doped) and x $\approx$ 0.10 (underdoped),
bookending the range of cubic phase in the compound. The results indicate no
deviation from fully gapped BCS-like behavior, eliminating several candidate
unconventional gap structures. Critical field values below 1 K and other
superconducting parameters are also presented. The introduction of disorder by
repeated particle irradiation with 5 MeV protons does not enhance $T_c$,
indicating that ferroelectric interactions do not compete with
superconductivity.
