Context. We demonstrate the calculation of solar wind electron bulk parameters based on recent observations by Solar Wind Analyser - Electron Analyser System on board Solar Orbiter. We use our methods to derive the electron bulk parameters in a time interval spanning several hours. We attempt a preliminary examination of the polytropic behavior of the electrons by analyzing the derived electron density and temperature. Moreover, we discuss the challenges in analyzing the observations due to the spacecraft charging and photo-electron contamination in the energy range below 10 eV. Aims. We derived bulk parameters for thermal solar wind electrons by analyzing Solar Orbiter observations and we investigated whether there is any typical polytropic model that is applicable to the electron density and temperature fluctuations. Methods. We used the appropriate transformations to convert the observations to velocity distribution functions in the instrument frame. We then derived the electron bulk parameters by: (a) calculating the statistical moments of the constructed velocity distribution functions and (b) fitting the constructed distributions with analytical expressions. We first tested our methods by applying them to an artificial data set, which we produced by using the forward modeling technique. Results. The forward model validates the analysis techniques we use to derive the electron bulk parameters. The calculation of the statistical moments and the fitting method determines bulk parameters that are identical (within the uncertainty limits) to the input parameters that we use to simulate the plasma electrons in the first place. An application of our analysis technique to the data reveals a nearly isothermal electron “core”. The results are affected by the spacecraft potential and the photo-electron contamination, which should be characterized in detail as part of future analyses.