The temperature of the local interstellar medium (LISM) is inferred from the analysis of interstellar neutral (ISN) atoms that enter and are detected in the inner heliosphere. Recent studies of the primary ISN helium population from the Interstellar Boundary Explorer (IBEX)-Lo sensor found a temperature of ∼7500 K. These studies assumed that the ISN helium atoms follow the Maxwell distribution in the LISM. Here, we check the impact of this assumption on the temperature. For this purpose, we use the kappa distribution as a model of the out-of-equilibrium state in the LISM. We compare the distribution functions for these distributions, accounting for the part of the distribution observed by IBEX. We identify the relationship between the κ index and temperature of the kappa distribution and show that there is a fundamental degeneracy between the two for the limited observations available. We find that a simple consistency with the IBEX data indicates that κ > 3.8, which likely limits the equivalent range of temperatures to 7500–11,000 K. These findings show that the physical state of the LISM ahead of the heliosphere may be substantially different than currently thought. Consequently, the result significantly impacts our understanding and future analyses of the interaction between the heliosphere and the LISM.