A finite-temperature relativistic fluid theory is used to analyse thez-dependent equilibrium state of a charge-neutralized electron beam in a diode with flat electrodes. Equilibrium is considered to be supported when the radial gradients of particle pressure are balanced against self-magnetic forces and the thermal energy of an electron is assumed to be much smaller than its rest mass energy. Under these conditions analytical expressions for the distribution of beam electrons are given in the pinched region. The density profile shows sharper pinching than a Bennett profile, as well as the enhancement of pinching resulting from an externally applied electric field.