The measurements of the solubility of carbon dioxide and oxygen in a commonly used room temperature ionic liquid, butyl methyl imidazolium tetrafluoroborate ([bmim] [BF4]), are reported as a function of temperature between 303 K and 343 K and at pressures close to atmospheric. A new experimental apparatus, based on a saturation method, is presented. The solubility is expressed in terms of molarities, mole fractions, and Henry's law coefficients. From their variation with temperature, the partial molar thermodynamic functions of solvation such as the standard Gibbs energy, the enthalpy, and the entropy are calculated. The precision of the experimental data, considered as the average absolute deviation of the Henry's law coefficients from appropriate smoothing equations, is 4% for oxygen and 3% for carbon dioxide.