The scaling between X-ray observables and mass for galaxy clusters and groups is instrumental for cluster based cosmology and an important probe for the thermodynamics of the intracluster gas . We calibrate a scaling relation between the weak lensing mass and X-ray spectroscopic temperature for 10 galaxy groups in the COSMOS field , combined with 55 higher mass clusters from the literature . The COSMOS data includes HST imaging and redshift measurements of 46 source galaxies per arcmin ^ { 2 } , enabling us to perform unique weak lensing measurements of low mass systems . Our sample extends the mass range of the lensing calibrated M–T relation an order of magnitude lower than any previous study , resulting in a power-law slope of 1.48 ^ { +0.13 } _ { -0.09 } . The slope is consistent with the self-similar model , predictions from simulations , and observations of clusters . However , X-ray observations relying on mass measurements derived under the assumption of hydrostatic equilibrium have indicated that masses at group scales are lower than expected . Both simulations and observations suggest that hydrostatic mass measurements can be biased low . Our external weak lensing masses provides the first observational support for hydrostatic mass bias at group level , showing an increasing bias with decreasing temperature and reaching a level of 30–50 % at 1 keV .