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We present a rigorous theoretical analysis of the ALICE measurement oflow-p_T direct-photon production in central lead-lead collisions at the LHCwith a centre-of-mass energy of \sqrt{s_{NN}}=2.76 TeV. Using NLO QCD, wecompute the relative contributions to prompt-photon production from differentinitial and final states and the theoretical uncertainties coming fromindependent variations of the renormalisation and factorisation scales, thenuclear parton densities and the fragmentation functions. Based on differentfits to the unsubtracted and prompt-photon subtracted ALICE data, weconsistently find T = 304 \pm 58 MeV and 309 \pm 64 MeV for the effectivetemperature of the quark-gluon plasma (or hot medium) at p_T \in [0.8;2.2] GeVand p_T \in [1.5;3.5] GeV as well as a power-law (p_T^{-4}) behavior for p_T >4 GeV as predicted by QCD hard scattering.

How robust is a thermal photon interpretation of the ALICE low-p_T data?