  We report on 13 new high-precision measurements of stellar diameters for
low-mass dwarfs obtained by means of near-infrared long-baseline interferometry
with PIONIER at the Very Large Telescope Interferometer. Together with accurate
parallaxes from Gaia DR2, these measurements provide precise estimates for
their linear radii, effective temperatures, masses, and luminosities. This
allows us to refine the effective temperature scale, in particular towards the
coolest M-dwarfs. We measure for late-type stars with enhanced metallicity
slightly inflated radii, whereas for stars with decreased metallicity we
measure smaller radii. We further show that Gaia DR2 effective temperatures for
M-dwarfs are underestimated by $\sim$ 8.2 % and give an empirical
$M_{G}$-$T_{\rm eff}$ relation which is better suited for M-dwarfs with $T_{\rm
eff}$ between 2600 and 4000 K. Most importantly, we are able to observationally
identify a discontinuity in the $T_{\rm eff}$-radius plane, which is likely due
to the transition from partially convective M-dwarfs to the fully convective
regime. We found this transition to happen between 3200 K and 3340 K, or
equivalently for stars with masses $\approx 0.23 M_{\odot}$. We find that in
this transition region the stellar radii are in the range from 0.18 to
0.42$R_{\odot}$ for similar stellar effective temperatures.
