The measurement of the direct photon transverse momentum spectrum in Pb-Pb collisions at √ s NN = 2.76 TeV with data taken by the ALICE experiment is presented. The measurement shows a clear direct-photon signal for 0-40% most central collisions below 4 GeV/c that can not be described by next-to-leading-order perturbative QCD (NLO pQCD) calculations. Above this value of p T the result is in agreement with pQCD predictions. The low p T signal is expected to have thermal photon contributions. The inverse slope parameter of an exponential fit is extracted as T LHC = 304±51 syst+stat MeV. For a baseline measurement the analysis is performed for protonproton collisions at √ s = 7 TeV and for peripheral (40-80%) Pb-Pb collisions. Both results show no low p T direct-photon signal and are in agreement with pQCD calculations.