We have studied the equilibrium and linear mechanical properties of model membranes of Escherichia coli built up as Langmuir monolayers of a native lipid extract using surface thermodynamics, fluorescence microscopy, and surface rheology measurements. The experimental study has been carried out at different temperatures across the physiological operative range 15-37 degrees C. Lipid phase coexistence has been revealed over a broad pressure range by fluorescence microscopy. The presence of ordered domains has been invoked to explain the emergence of shear elasticity accompanying the hydrostatic compression elasticity typical of fluid monolayers. The surface rheology measurements point out the soft character of E. coli membranes; i.e., upon deformation they react as a near-ideal compliant body with minimal energy dissipation, thus optimizing the effectiveness of external stresses in producing membrane deformations. These mechanical features appear to be independent of temperature, suggesting the existence of a passive thermoregulation mechanism.