We use a high-temperature expansion to explore spin correlations around a single hole in a two-dimensional lattice filled with a hard-core two-component bose gas. We find that the spins around the hole develop ferromagnetic order and quantify the degree of polarization at temperatures of the order of the hopping energy, finding a measurably nonzero polarization. We also discuss the effect of fixing the overall magnetization of the system for finite-sized systems. © 2013 American Physical Society.