The thermal stability of the magnetic nano-skyrmion lattice in the monolayer Fe/Ir(111) is investigated using temperature dependent spin-polarized scanning tunneling microscopy. Our experiments show that the skyrmion lattice disappears at a temperature of T_{c}=27.8 K, indicating a loss of long-range magnetic order. At second-layer iron islands the lattice is pinned and local order persists at temperatures above T_{c}. The findings are explained in terms of the complex magnetic interactions involved in the formation of the skyrmion lattice.