  The classical T Tauri star AA Tau presented photometric variability
attributed to an inner disk warp, caused by the interaction between the inner
disk and an inclined magnetosphere. Previous studies of NGC 2264 have shown
that similar photometric behavior is common among CTTS.
  The goal of this work is to investigate the main causes of the observed
photometric variability of CTTS in NGC 2264 that present AA Tau-like light
curves, and verify if an inner disk warp could be responsible for their
variability. We investigate veiling variability in their spectra and u-r color
variations and estimate parameters of the inner disk warp using an occultation
model proposed for AA Tau. We compare infrared and optical light curves to
analyze the dust responsible for the occultations. AA Tau-like variability is
transient on a timescale of a few years. We ascribe it to stable accretion
regimes and aperiodic variability to unstable accretion regimes and show that a
transition, and even coexistence, between the two is common. We find evidence
of hot spots associated with occultations, indicating that the occulting
structures could be located at the base of accretion columns. We find average
values of warp maximum height of 0.23 times its radial location, consistent
with AA Tau, with variations of on average 11% between rotation cycles. We show
that extinction laws in the inner disk indicate the presence of grains larger
than interstellar grains.
  The inner disk warp scenario is consistent with observations for all but one
periodic star in our sample. AA Tau-like systems comprise 14% of CTTS observed
in NGC 2264, though this increases to 35% among systems of mass
0.7M_sun<M<2.0M_sun. Assuming random inclinations, we estimate that nearly all
systems in this mass range likely possess an inner disk warp, possibly because
of a change in magnetic field configurations among stars of lower mass.
