We report results of the first laser collimation of a thermal beam of Fe atoms on the leaky ^5D_4 -> ^5F_5 transition, with both parallel linear pi^x-pi^x and crossed linear pi^x-pi^y laser polarization configurations. The measured atomic beam divergence is compared to a rate-equation model and a quantum Monte Carlo model. The experimental values for the divergence are limited by the finite laser line width, which is comparable to the natural line width of the Fe atom. In general, flux decreases with higher intensities, showing the effect of the leaky transition. At the best beam collimation alpha_RMS = 0.17 mrad, which is for a detuning of delta = –Gamma and a saturation parameter of s = 6, the flux decreased to approximately 70%. Highest flux was measured for a detuning of delta = –2Gamma and s = 4, reaching 135% of the uncooled value. From our measurements we estimate the total leak rate to be 1/(240 ± 40), which is in good agreement with the literature value of 1/244. The crossed linear polarization configuration is the better choice, with a slightly better collimation but the same atomic beam flux. Plugging of the largest leak would increase the flux to at least 80% of the closed transition value, resulting in better contrast for atom lithography.