We report the results of x-ray photon correlation spectroscopy (XPCS) experiments on multilayers of a photosensitive azo-polymer which can be softened by photoisomerization. Time correlation functions have been measured at different temperatures and momentum transfers (q) and under different illumination conditions (dark, UV or visible). The correlation functions are well described by the Kohlrausch-Williams-Watts (KWW) form with relaxation times that are proportional to q(-1). The characteristic relaxation times follow the same Vogel-Fulcher-Tammann law describing the bulk viscosity of this polymer. The out-of-equilibrium relaxation dynamics following a UV photoperturbation are accelerated, which is in agreement with a fluidification effect previously measured by rheology. The transient dynamics are characterized by two times correlation function, and dynamical heterogeneity is evidenced by calculating the variance χ of the degree of correlation as a function of ageing time. A clear peak in χ appears at a well defined time τ(C) which scales with q(-1) and with the ageing time, in a similar fashion as previously reported in colloidal suspensions [O. Dauchot, Phys. Rev. Lett. 95, 265701 (2005)]. From an accurate analysis of the correlation functions we could demonstrate a temperature and light dependent cross-over from compressed KWW to simple exponential behavior.