  We consider the non-commutative inflation model of [3] in which it is the
unconventional dispersion relation for regular radiation which drives the
accelerated expansion of space. In this model, we study the evolution of linear
cosmological perturbations through the transition between the phase of
accelerated expansion and the regular radiation-dominated phase of Standard
Cosmology, the transition which is analogous to the reheating period in scalar
field-driven models of inflation. If matter consists of only a single
non-commutative radiation fluid, then the curvature perturbations are constant
on super-Hubble scales. On the other hand, if we include additional matter
fields which oscillate during the transition period, e.g. scalar moduli fields,
then there can be parametric amplification of the amplitude of the curvature
perturbations. We demonstrate this explicitly by numerically solving the full
system of perturbation equations in the case where matter consists of both the
non-commutative radiation field and a light scalar field which undergoes
oscillations. Our model is an example where the parametric resonance of the
curvature fluctuations is driven by the oscillations not of the inflaton field,
but of the entropy mode
