There is abundant evidence that heating processes in the central regions of elliptical galaxies have both prevented large–scale cooling flows and assisted in the expulsion of metal rich gas. We now know that each such spheroidal system harbours in its core a massive black hole weighing ca. 0.13% of the mass in stars and also know that energy was emitted by each of these black holes with an efficiency exceeding 10% of its rest mass. Since, if only 0.5% of that radiant energy were intercepted by the ambient gas, its thermal state would be drastically altered, it is worth examining in detail the interaction between the out–flowing radiation and the equilibrium or inflowing gas. On the basis of detailed hydrodynamic computations we find that relaxation oscillations are to be expected with the radiative feedback quite capable of regulating both the growth of the central black hole and also the density and thermal state of the gas in the galaxy. Mechanical input of energy by jets may assist or dominate over these radiative effects.We propose specific observational tests to identify systems which have experienced strong bursts of radiative heating from their central black holes.