Spacecraft observations allow us to reconstruct the velocity distributions of space plasmas, which fully describe the kinetic state of the plasma. Space plasmas often exist in stationary states out of equilibrium, which are typically described by kappa distributions. Thus, the kappa index and temperature that govern these distributions are parameters that need to be determined for a full and accurate description of these plasmas. In this study, we demonstrate a novel and reliable way to determine the kappa index and temperature of plasma distribution functions constructed from counts observed in a narrow energy range by typical electrostatic sensors. Our method applies to cases in which the high-energy tail of the plasma is observed with significant uncertainty, or not observed at all. For the validation of our method, we produce pseudo-observations for typical input plasma parameters, specifically considering the design of the ion plasma instrument SWA-PAS on board the Solar Orbiter mission. Our method reliably estimates the relevant plasma parameters by fitting the angular spread of the distribution in a narrow energy range around the core bulk energy. We compare the output of our technique with the input parameters used to generate artificial data for a selected range of the kappa index and the temperature, and for a bulk energy typical for the solar wind. In addition, we study the effects of Poisson errors on the instrument's counting statistics, test our method against Helios 2 measurements, and discuss its potential applications and limitations.