  We present 3, 15, and 33 GHz imaging towards galaxy nuclei and extranuclear
star-forming regions using the Karl G. Jansky Very Large Array as part of the
Star Formation in Radio Survey. With $3-33$ GHz radio spectra, we measured the
spectral indices and corresponding thermal (free-free) emission fractions for a
sample of 335 discrete regions having significant detections in at least two
radio bands. After removing 14 likely background galaxies, we find that the
median thermal fraction at 33 GHz is $92 \pm 0.8\%$ with a median absolute
deviation of $11\%$, when a two-component power-law model is adopted to fit the
radio spectrum. Limiting the sample to 238 sources that are confidently
identified as star-forming regions, and not affected by potential AGN
contamination (i.e., having galactocentric radii $r_{\rm G} \geq 250$ pc),
results in a median thermal fraction of $93 \pm 0.8 \%$ with a median absolute
deviation of $10\%$. We further measure the thermal fraction at 33 GHz for 163
regions identified at 7" resolution to be $94 \pm 0.8 \%$ with a median
absolute deviation of $8\%$. Together, these results confirm that free-free
emission dominates the radio spectra of star-forming regions on scales up to
$\sim$500 pc in normal star-forming galaxies. We additionally find a factor of
$\sim$1.6 increase in the scatter of the measured spectral index and thermal
fraction distributions as a function of decreasing galactocentric radius. This
trend is likely reflective of the continuous star-formation activity occurring
in the galaxy centers, resulting a larger contribution of diffuse nonthermal
emission relative to star-forming regions in the disk.
