High-TC superconducting (HTS) hot electron bolometers (HEB) are promising THz mixers due to their large expected bandwidth and low local oscillator (LO) power requirements at 60-80 K operating temperature. To obtain HEB efficient mixing, it is mandatory to grow very thin high quality HTS films leading to good micro or nano-bolometer superconducting properties. The challenge for Y-Ba-Cu-O resides, however, in the chemical reactivity of the material and the related aging effects. Early HEB models described the device in terms of thermal reservoirs only, namely the electrons and the phonons of the superconductor. The electron-phonon interaction time, which drives the HEB mixer ultimate response, is 1-2 ps for Y-Ba-Cu-O, with an expected bandwidth close to 100 GHz. Recently, we introduced the hot spot model for Y-Ba-Cu-O HEBs, taking - more realistically - the spatial dependence of the electron temperature along the nano-bolometer (or constriction) length into account. From DC analysis, the I-V characteristics could be deduced. In this paper, we further consider a full description of the constriction impedance at THz frequencies, which allows to work out the mixer performance in terms of double sideband noise temperature TDSB and conversion gain G. For a constriction of technologically achievable dimensions, i.e., 400 nm long x 400 nm wide x 35 nm thick, minimum TDSB = 1900 K at 9 μW LO power, with G = -9.5 dB, is obtained at 400 GHz, assuming impedance matching with a selfcomplementary planar antenna.