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We present the results of direct measurements of the temperature resolution of an HEB receiver operating at 810 GHz, in both continuum and spectroscopic modes. In the continuum mode, the input of the receiver was switched between black bodies with different physical temperatures. With a system noise temperature of around 1100 K, the receiver was able to resolve loads which differed in temperature by about 1 K over an integration time of 5 seconds. This resolution is significantly worse than the value of 0.07 K given by the radiometer equation. In the spectroscopic mode, a gas cell filled with carbonyl sulphide (OCS) gas was used and the emission line at 813.3537060 GHz was measured using the receiver in conjunction with a digital spectrometer. From the observed spectra, we determined that the measurement uncertainty of the equivalent emission temperature was 2.8 K for an integration time of 0.25 seconds and a spectral resolution of 12 MHz, compared to a 1.4 K temperature resolution given by the radiometer equation. This relative improvement is due to the fact that at short integration times the contribution from 1/f noise and drift are less dominant. In both modes, the temperature resolution was improved by about 40% with the use of a feedback loop which adjusted the level of an injected microwave radiation to maintain a constant operating current of the HEB mixer. This stabilization scheme has proved to be very effective to keep the temperature resolution of the HEB receiver to close to the theoretical value given by the radiometer equation. [ABSTRACT FROM AUTHOR]