  We studied the isotropic Compton profile of the prototypical oxide VO$_2$
across the temperature induced electronic and structural phase transition at
T$_C$ $\approx$ 340 K. We show that the phase transition leaves an observable
signal, which facilitates Compton scattering studies of electronic structure
and phase transitions in complex solids in powder form. We compare the
experimental results with density functional theory calculations and find
agreement in the shape of the difference profile, although the amplitude of the
observed features is overestimated. The origin of the disagreement is discussed
and we argue that it mainly originates mostly correlation effects beyond our
current calculations and possibly to some extent, from thermal motion.
