  We offer a unifying theory for turbulent purely internally heated convection,
generalizing the unifying theories of Grossmann and Lohse (2000, 2001) for
Rayleigh--B\'enard turbulence and of Shishkina, Grossmann and Lohse (2016) for
turbulent horizontal convection, which are both based on the splitting of the
kinetic and thermal dissipation rates in respective boundary and bulk
contributions. We obtain the mean temperature of the system and the Reynolds
number (which are the response parameters) as function of the control
parameters, namely the internal thermal driving strength (called, when
nondimensionalized, the Rayleigh--Roberts number) and the Prandtl number. The
results of the theory are consistent with our direct numerical simulations.
