Thermodynamic properties of the spin-1/2 Heisenberg ferromagnet are calculated by using Handscomb's Monte Carlo method. Several methods of analyses are used to determine critical properties of the model. For a square lattice we find that the susceptibility diverges exponentially at zero temperature. That is, chi approximately exp[b(J/k(B)T)] with the constant b = 4.5 +/- 0.5, which is lower than the prediction (b = 2-pi) of a modified spin-wave theory. For the simple-cubic lattice, we find that the critical temperature k(B)T(c)/J = 1.68 +/- 0.01, and the ratio of the exponents gamma/nu = 2.0 +/- 0.05, which are in good agreement with the estimates of the high-temperature series-expansion method.