In this paper we investigate the hot end of the HB, presenting evolutionary constraints concerning the CM diagram location and the gravity of hot HB stars. According to the adopted evolutionary scenario, we predict an upper limit for HB temperatures of about logTe = 4.45, remarkably cooler than previous estimates. We find that such a theoretical prescription appears in good agreement with available observational data concerning both stellar temperatures and gravities. ; Comment: postscript file of 10 pages plus 1 tables,rep.1 5 figures will be added later as postscript file The tex file and the other two not postscript figures are available upon request at scilla@vaxfe.fe.infn.it, rep.1