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 < r500c. In addition, we find that many merger shocks can propagate with almost constant velocity to very large radii r ≫ r500c, 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.