Quantitative phase microscopy by digital holography provides direct access to the phase profile of a transparent subject with high precision. This is useful for observing phenomena that modulate phase, but are otherwise difficult or impossible to detect. In this letter, a carefully constructed digital holographic apparatus is used to measure optically induced thermal lensing with an optical path difference precision of less than 1 nm. Furthermore, by taking advantage of the radial symmetry of a thermal lens, such data are processed to determine the absorption coefficient of transparent media with precisions as low as 1 \times 10^{-5} cm^{-1} using low power (30 mW) continuous wave (CW) excitation.