Quantum two-dimensional Heisenberg ferromagnetic systems were studied using the Handscomb Monte Carlo approach. Temperatures ranged from 0.3 to 4.0 J. The large system sizes used made it possible to apply scaling methods and to calculate infinite system susceptibility values for temperatures considerably lower than have been studied elsewhere. The internal energy was found to be essentially size-independent for all temperatures. Comparisons were drawn between the Godfrin et al. (1988) experimental observation of the quantum two-dimensional ferromagnetism in thin films of ³He and the authors results for temperature dependence of simulated susceptibility. The existence of several essential similarities was verified; for example, the non-exponential low-temperature behaviour of chi T. Their results for susceptibility and energy were compared with other numerical simulations and various theoretical predictions. The comparisons have enabled them to define temperature regions where high and low temperature approximations are valid. Monte Carlo results also fill the gap between the approximations.