  The diffuse plasma inside clusters of galaxies has X-ray emitting
temperatures of a few keV. The physical mechanisms that heat this intracluster
medium (ICM) to such temperatures include the accretion shock at the periphery
of a galaxy cluster, the shocks driven by merger events, as well as a somewhat
overlooked mechanism -- the dissipation of intracluster turbulent motions. We
study the relative role of these heating mechanisms using galaxy clusters in
Lagrangian tracer particle re-simulations of the Omega500 cosmological
simulation. We adopt a novel analysis method of decomposing the temperature
increase at each time step into the contribution from dissipative heating and
that from adiabatic heating. In the high-resolution spatial-temporal map of
these heating rates, merger tracks are clearly visible, demonstrating the
dominant role of merger events in heating the ICM. The dissipative heating
contributed by each merger event is extended in time and also occurs in the
rarefaction regions, suggesting the importance of heating by the dissipation of
merger-induced turbulence. Quantitative analysis shows that turbulence heating,
rather than direct heating at merger shocks, dominates the temperature increase
of the ICM, especially at inner radii $r < r_{\rm 500c}$. In addition, we find
that many merger shocks can propagate with almost constant velocity to very
large radii $r \gg r_{\rm 500c}$, some even reach and join with the accretion
shock and becoming the outer boundary of the ICM. Altogether, these results
suggest that the ICM is heated more in an `inside-out' fashion rather than
`outside-in' as depicted in the classical smooth accretion picture.
