We present Goddard High Resolution Spectrograph observations of the M8 Ve star VB 10 (= Gl 752B), located very near the end of the stellar main sequence, and its dM3.5 binary companion Gl 752A. These coeval stars provide a test bed for studying whether the outer atmospheres of stars respond to changes in internal structure as stars become fully convective near mass 0.3 Msun (about spectral type MS), where the nature of the stellar magnetic dynamo presumably changes, and near the transition from red to brown dwarfs near mass 0.08 Msun (about spectral type M9), when hydrogen burning ceases at the end of the main sequence. We obtain upper limits for the quiescent emission of VB 10 but observe a transition region spectrum during a large flare, which indicates that some type of magnetic dynamo must be present. Two indirect lines of evidence scaling from the observed X-ray emission and scaling from a time-resolved flare on AD Le suggest that the fraction of the stellar bolometric luminosity that heats the transition region of VB 10 outside of obvious flares is comparable to, or larger than, that for Gl 752A. This suggests an increase in the magnetic heating rates, as measured by Lline/Lbol ratios, across the radiative/convective core boundary and as stars approach the red/brown dwarf boundary. These results provide new constraints for dynamo models and models of coronal and transition-region heating in late-type stars.