Single-component, homogeneous model chromospheres that are consistent with high-resolution profiles of the Ca II K line calibrated in surface flux units for three dMe and 2 dM stars observed at quiescent times are constructed. The models reveal several systematic trends. Large values of the ratio of T(min) to T(eff) are derived, indicating a large amount of nonradiative heating present in the upper photospheres of M dwarf stars. It is also found that the lower chromospheric temperature gradient is similar for all the M dwarf stars. Since for the models here the chromospheric K line emission strength is most sensitive to the total amount of chromospheric material present within the approximate temperature range T(min)-6000 K, increasing the emission strength is not simply due to increasing chromospheric temperature gradients. It is also found that both the electron density and electron temperature at one thermalization length in the K line below the top of the chromospheres are greater in the dMe stars than in the dM stars. The M dwarf models here have microturbulent velocities between 1 and 2 km/sec, which are much smaller than for solar chromosphere models.