The results of Monte Carlo simulations of the electron noise in lightly doped and strongly compensated n-type InSb are presented. The strong electron scattering by ionized impurities is established to change essentially the electron distribution function, spectral density of velocity fluctuations and the dependence of noise temperature on the electric field strength. It is found that the electron noise temperature in strongly compensated InSb with low electron density at liquid nitrogen temperature is close to the lattice temperature in a wide range of electric field strength in which the electron gas cooling effect takes place. The increase of electron density is shown to weaken the electron gas cooling effect due to more intensive electron-electron collisions stimulating delocalization of electrons from the bottom of the conduction band. A satisfactory agreement between calculations and available experimental data is obtained.