The intermediate frequency (IF) characteristics, the frequency dependent IF impedance, and the mixer conversion gain of a small area hot electron bolometer (HEB) have been measured and modeled. The device used is a twin slot antenna coupled NbN HEB mixer with a bridge area of 1×0.15μm2, and a critical temperature of 8.3K. In the experiment the local oscillator frequency was 1.300THz, and the (IF) 0.05-10GHz. We find that the measured data can be described in a self-consistent manner with a thin film model presented by Nebosis et al. [Proceedings of the Seventh International Symposium on Space Terahertz Technology, Charlottesville, VA, 1996 (unpublished), pp. 601-613], that is based on the two temperature electron-phonon heat balance equations of Perrin-Vanneste [J. Phys. (Paris) 48, 1311 (1987)]. From these results the thermal time constant, governing the gain bandwidth of HEB mixers, is observed to be a function of the electron-phonon scattering time, phonon escape time, and the electron temperature. From the developed theory the maximum predicted gain bandwidth for a NbN HEB is found to be 5.5-6GHz. In contrast, the gain bandwidth of the device under discussion was measured to be ˜2.3GHz which, consistent with the outlined theory, is attributed to a somewhat low critical temperature and nonoptimal film thickness (6nm).