  The ALICE detector at the LHC is used to study the properties of the
Quark-Gluon Plasma produced in heavy-ion collisions. As a reference
measurement, also the analysis of proton-proton (pp) collisions is very
important. In the study presented here, event-by-event fluctuations of the mean
transverse momentum are analysed in pp collisions at sqrt(s) = 0.9, 2.76 and 7
TeV, and Pb-Pb collisions at sqrt(s_NN) = 2.76 TeV as a function of the
charged-particle multiplicity. In both systems, dynamical fluctuations beyond
the statistical expectation are observed. In pp collisions, no significant
dependence on collision energy is found, even in comparison to inclusive
results at much lower collision energies. Likewise, central A-A collisions show
only little dependence on collision energy. The multiplicity dependence
observed in peripheral Pb-Pb data is in agreement with that in pp collisions.
Going to more central Pb-Pb collisions, a clear deviation from this trend is
found, reaching a significant reduction of the fluctuations in most central
collisions. Comparisons to Monte Carlo event generators show good agreement in
pp, but rather large differences in Pb-Pb collisions.
