  We detected millihertz quasi-periodic oscillations (QPOs) in an XMM-Newton
observation of the neutron-star low-mass X-ray binary 4U 1636-53. These QPOs
have been interpreted as marginally-stable burning on the neutron-star surface.
At the beginning of the observation the QPO was at around 8 mHz, together with
a possible second harmonic. About 12 ks into the observation a type I X-ray
burst occurred and the QPO disappeared; the QPO reappeared ~25 ks after the
burst and it was present until the end of the observation. We divided the
observation into four segments to study the evolution of the spectral
properties of the source during intervals with and without mHz QPO. We find
that the temperature of the neutron-star surface increases from the QPO segment
to the non-QPO segment, and vice versa. We also find a strong correlation
between the frequency of the mHz QPO and the temperature of a black-body
component in the energy spectrum representing the temperature of neutron-star
surface. Our results are consistent with previous results that the frequency of
the mHz QPO depends on the variation of the heat flux from the neutron star
crust, and therefore supports the suggestion that the observed QPO frequency
drifts could be caused by the cooling of deeper layers.
