We set out to determine stellar labels from low-resolution survey spectra of hot stars, specifically OBA stars with Teff>~7500K. This fills a gap in the scientific analysis of large spectroscopic stellar surveys such as LAMOST, which offers spectra for millions of stars at R~1800 and covering 3800{AA}-9000{AA}. We first explore the theoretical information content of such spectra for determining stellar labels, via the Cramer-Rao bound. We show that in the limit of perfect model spectra and observed spectra with S/N~50-100, precise estimates are possible for a wide range of stellar labels: not only the effective temperature Teff, surface gravity logg, and projected rotation velocity vsini, but also the micro-turbulence velocity vmic , Helium abundance NHe=Ntot and the elemental abundances [C/H], [N/H], [O/H], [Si/H], [S/H], and [Fe/H]. Our analysis illustrates that the temperature regime of Teff~9500K is challenging, as the dominant Balmer and Paschen line strength vary little with Te . We implement the simultaneous fitting of these 11 stellar labels to LAMOST hot-star spectra using the PAYNE approach, drawing on Kurucz's ATLAS12/SYNTHE LTE spectra as the underlying models. We then obtain stellar parameter estimates for a sample of about 330000 hot stars with LAMOST spectra, an increase by about two orders of magnitude in sample size. Among them, about 260000 have S/N>5 Gaia parallaxes, and their luminosities imply that >~95% among them are luminous star, mostly on the main sequence; the rest reflects lower luminosity evolved stars, such as hot subdwarfs and white dwarfs. We show that the fidelity of the results, particularly for the abundance estimates, is limited by the systematics of the underlying models, as they do not account for NLTE effects. Finally, we show the detailed distribution of v sin i of stars with 8000-15000K, illustrating that it extends to a sharp cut-off at the critical rotation velocity, vcrit, across a wide range of temperatures.