The specific heat (cp) of the dilute antiferromagnet FexZn1-xF2 has been measured in absence of external magnetic fields for x = 0, 0.26, 0.31, 0.34, 0.36, 0.38, 0.41, 0.45, 0.56, 0.88, 0.97, and 1.0. For x > 0.45, a sharp peak associated to the antiferromagnetic (AF) phase transition at TN(x) is the only observed feature. For 0.31 ≤ x ≤ 0.41, this peak becomes smaller with decreasing x and a rounded bump appears at higher temperatures T. Closer to the percolation concentration (xp = 0.24), the peak characteristic of the AF phase transition disappears and the rounded bump becomes the only observed feature. The low-Tcp behavior confirms a crossover from AF long range order at large x to a spin glass behavior close to xp. At intermediate x, the low-T joint signature of both phenomena indicates a coexistence of AF order and a cluster-glass phase. The x-dependence of the Néel temperature was accounted for using a simple phenomenological model.