The spatial emission from the core of cooling-flow clusters of galaxies is inadequately described by a β-model. Spectrally, the central region of these clusters is well approximated with a two-temperature model, where the inner temperature represents the multiphase status of the core and the outer temperature is a measure of the ambient gas temperature. Following this observational evidence, I extend the use of the β-model to a two-phase gas emission, where the two components coexist within a boundary radius rcool and the ambient gas alone fills the volume shell at a radius above rcool. This simple model still provides an analytic expression for the total surface brightness profile (Note in the first term the different sign with respect to the standard β-model.) Based upon a physically meaningful model for the X-ray emission, this formula can be used (i) to improve significantly the modelling of the surface brightness profile of cooling flow clusters of galaxies when compared to the standard β-model results, (ii) to constrain properly the physical characteristics of the intracluster plasma in the outskirts, like, e.g., the ambient gas temperature.