It is argued that the most appropriate definition of the local temperature T(r) for the ground state of an electronic system is provided by the formula 3/2rho(r)kT(r)=1/8∑i[(∇rhoi.∇rhoi)/rhoi], where rho(r) is the total electron density and the rhoi are Kohn-Sham orbital densities. T(r) is everywhere non-negative. For atoms, T(r) is nearly stepwise constant. T(r) behaves very much like the Politzer average local ionization energy index. Accordingly, T(r) measures reactivity toward attack by an electron-attracting reagent. Exchange energies and Compton profiles are calculated for several atoms using this definition of the local temperature.