We studied the temperature dependence of the diagonal double-stripe spin order in 1 and 2 unit cell thick layers of FeTe grown on the topological insulator Bi2Te3 via spin-polarized scanning tunneling microscopy. The spin order persists up to temperatures which are higher than the transition temperature reported for bulk Fe1+yTe with lowest possible excess Fe content y. The enhanced spin order stability is assigned to a strongly decreased y with respect to the lowest values achievable in bulk crystal growth, and effects due to the interface between the FeTe and the topological insulator. The result is relevant for understanding the recent observation of a coexistence of superconducting correlations and spin order in this system.