  Rayleigh-B\'enard convection in the turbulent regime is studied using
statistical methods. Exact evolution equations for the probability density
function of temperature and velocity are derived from first principles within
the framework of the Lundgren-Monin-Novikov hierarchy known from homogeneous
isotropic turbulence. The unclosed terms arising in the form of conditional
averages are estimated from direct numerical simulations. Focusing on the
statistics of temperature, the theoretical framework allows to interpret the
statistical results in an illustrative manner, giving deeper insight into the
connection between dynamics and statistics of Rayleigh-B\'enard convection. The
results are discussed in terms of typical flow features and the relation to the
heat transfer.
