We address the degeneracy of the ground state multiplet on the 5d(1) Re6+ ion in double perovskite Ba2MgReO6 using a combination of specific heat measurements and density functional calculations. For Ba2MgReO6, two different ground state multiplets have previously been proposed-a quartet (with degeneracy N = 4) (Hirai and Hiroi 2019 J. Phys. Soc. Japan 88 064712) and a doublet (N = 2) (Marjerrison et al 2016 Inorg. Chem. 55 10701). Here we employ two independent methods for the estimation of phonon contribution in heat capacity data to obtain the magnetic entropy S-mag, which reflects the degeneracy of the ground state multiplet N through S-mag = RlnN. In both cases, we obtain that in the temperature range covering 2 to 120 K the released entropy is better described by S-mag = Rln2. The detailed nature of the ground state multiplet in Ba2MgReO6 remains an open question.