  We report results of the numerical solution by the Euler method of the system
of heat balance equations written in recurrent form for the superconducting
hot-electron bolometer (HEB) embedded in an electrical circuit. By taking into
account the dependence of the HEB resistance on the transport current we have
been able to calculate rigorously the RF heating efficiency, absorbed local
oscillator (LO) power and conversion gain of the HEB mixer. We show that the
calculated conversion gain is in excellent agreement with the experimental
results, and that the substitution of the calculated RF heating efficiency and
absorbed LO power into the expressions for the conversion gain and noise
temperature given by the analytical small-signal model of the HEB yields
excellent agreement with the corresponding measured values.
