We match the Hagedorn/deconfinement temperature of planar N = 4 super Yang-Mills (SYM) on ℝ × S³ to the Hagedorn temperature of string theory on AdS₅ × S⁵. The match is done in a near-critical region where both gauge theory and string theory are weakly coupled. On the gauge theory side we are taking a decoupling limit found in [7] in which the physics of planar N = 4 SYM is given exactly by the ferromagnetic XXX_1/2 Heisenberg spin chain. We find moreover a general relation between the Hagedom/deconfinement temperature and the thermodynamics of the Heisenberg spin chain. On the string theory side, we identify the dual limit which is taken of string theory on a maximally symmetric pp-wave background with a flat direction, obtained from a Penrose limit of AdS₅ × S⁵. We compute the Hagedorn temperature of the string theory and find agreement with the Hagedorn/deconfinement temperature computed on the gauge theory side. Finally, we discuss a modified decoupling limit in which planar N = 4 SYM reduces to the XXX_1/2 Heisenberg spin chain with an external magnetic field.