Star formation in galaxies at the center of cooling-flow galaxy clusters is an important phenomenon in the context of formation and evolution of massive galaxies in the Universe . Yet , star formation rates ( SFRs ) in such systems continue to be elusive . We use our Bayesian-motivated spectral energy distribution ( SED ) -fitting code , bayescool , to estimate the plausible SFR values in the brightest cluster galaxy of a massive , X-ray luminous galaxy cluster , Phoenix . Previous studies of Phoenix have resulted in the highest measurement of SFR for any galaxy , with the estimates reaching up to 1000 ~ { } M _ { \odot } ~ { } \mathrm { yr } ^ { -1 } . However , a very small number of models have been considered in those studies . bayescool allows us to probe a large parameter space . We consider two models for star formation history , instantaneous bursts and continuous star formation , a wide range of ages for the old and the young stellar population , along with other discrete parameters , such as the initial mass function , metallicities , internal extinction and extinction law . We find that in the absence of any prior except that the maximum cooling rate < 3000 ~ { } M _ { \odot } ~ { } \mathrm { yr } ^ { -1 } , the SFR lies in the range ( 2230 - 2890 ) ~ { } M _ { \odot } ~ { } \mathrm { yr } ^ { -1 } . If we impose an observational prior on the internal extinction , E ( B-V ) \leq 0.6 , the best-fit SFR lies in ( 454 - 494 ) M _ { \odot } ~ { } \mathrm { yr } ^ { -1 } , and we consider this as the most probable range of SFR values for Phoenix . The SFR dependance on the extinction is a reflection of the standard age-extinction degeneracy , which can be overcome by using a prior on one of the two quantities in question . Keywords : galaxies : clusters : intracluster medium ; galaxies : clusters : individual : SPT-CLJ2344-4243 ; galaxies : formation ; galaxies : star formation ; ISM : ) dust , extinction