Ultrasmall nanosized silicate grains are likely to be highly abundant in the interstellar medium. From sporadically absorbing energy from ultraviolet photons, these nanosilicates are subjected to significant instantaneous temperature fluctuations. These stochastically heated nanograins subsequently emit in the infrared. Previous estimates of the extent of the heating and emission have relied on empirical fits to bulk silicate heat capacities. The heat capacity of a system depends on the range of available vibrational modes, which for nanosized solids is dramatically affected by the constraints of finite size. Although experimental vibrational spectra of nanosilicates is not yet available, we directly take these finite size effects into account by using accurate vibrational spectra of low-energy nanosilicate structures from quantum chemical density functional theory calculations. Our results indicate that the heat capacities of ultrasmall nanosilicates are smaller than previously estimated, which would lead to a higher temperature and more intense infrared emission during stochastic heating. Specifically, we find that stochastically heated grains ultrasmall nanosilicates could be up to 35-80 K hotter than previously predicted. Our results could help to improve the understanding of infrared emission from ultrasmall nanosilicates in the ISM, which could be observed by the James Webb Space Telescope.