Suprathermal populations are ubiquitous in the solar wind, indicating plasma states out of thermal equilibrium, and an excess of free energy expected to enhance the kinetic instabilities. The generally accepted representation of Kappa distributions usually invoked to describe these populations in space plasma physics allows for two different alternatives, namely assuming the temperature either dependent or independent on the k-index of the distribution. Here we demonstrate that only a k-dependent temperature confirms the expectations providing a systematic stimulation of the temperature anisotropy instabilities, and present observational evidences in the favor of this approach.