We revisit the estimation of the power deposited by the electron cloud (EC) in the arc dipoles of the LHC by means of simulations. We adopt, as simulation input, a set of electron-related parameters closely resembling those used in recent simulations at CERN [1]. We explore values for the bunch population Nb in the range 0.4 x 10^11 2 and Nb > 1.5 x 10^11 taken in combination. The rediffused component of the secondary electron emission spectrum plays a significant role: if we artificially suppress this component while keeping delta max fixed, dPbar/dz is roughly cut in half for most values of Nb explored here, and in this case we find good agreement with the results in Ref. 1, as expected. We provide a fairly detailed explanation of the mechanism responsible for such a relatively large effect. We assess the sensitivity of our results to numerical simulation parameters, and to physical parameters such as the photoelectric yield, bunch train length, etc. Owing to the lack of detailed knowledge of the electron emission spectrum, the sensitivity of dPbar/dz to the rediffused component appears to be the most significant source of uncertainty in our results. Nevertheless, taking our results as a whole, the condition delta max <= 1.2 seems to be a conservative requirement for the cooling capacity not to be exceeded.