We present measurements of the masses of 20 X-ray luminous clusters of galaxies at intermediate redshifts , determined from a weak lensing analysis of deep archival R -band data obtained using the Canada-France-Hawaii-Telescope . Compared to previous work , our analysis accounts for a number of effects that are typically ignored , but can lead to small biases , or incorrect error estimates . We derive masses that are essentially model independent and find that they agree well with measurements of the velocity dispersion of cluster galaxies and with the results of X-ray studies . Assuming a power law between the lensing mass and the X-ray temperature , M _ { 2500 } \propto T ^ { \alpha } , we find a best fit slope of \alpha = 1.34 ^ { +0.30 } _ { -0.28 } . This slope agrees with self-similar cluster models and studies based on X-ray data alone . For a cluster with a temperature of kT = 5 keV we obtain a mass M _ { 2500 } = ( 1.4 \pm 0.2 ) \times 10 ^ { 14 } h ^ { -1 } \hbox { M$ { } _ { \odot } $ } in fair agreement with recent Chandra and XMM studies .