The paper is aimed at investigating the role of inhomogeneous heating of the neutral gas in a constricted glow discharge in neon and argon. It is shown that inhomogeneous heating is not the primary cause of constriction in specified gases at pressures of tens and hundreds Torr cm and reduced currents not exceeding 100-200 mA cm^-1. Constriction of the positive column occurs even with an insignificant gas heating in a pulsed regime. An abrupt constriction is caused by the nonlinear dependence of the ionization number on the electron density. In mentioned discharge conditions the frequency of electron-electron collisions is comparable to the electron energy relaxation frequency due to elastic electron-atom collisions. Thermal effects play a secondary role in the formation of a constricted discharge. At the same time, inhomogeneous gas heating in argon is more notable than in neon. Unlike neon, stationary argon discharge loses spatial stability in a vertically oriented tube as the pressure and current increase and a buoyancy effect takes place in a horizontal orientation. Such difference in the behavior of constricted neon and argon discharges is mainly caused by the difference in shape of elastic electron-atom collision cross sections. Interferometric methods allowed to study the temperature field of neutral atoms, dynamics of both gas heating and ascent of constricted cord. Observed effects are interpreted on the basis of the heat equation and the Navier-Stokes equation. Comparison of experimental and theoretical results shows good agreement.