  Hot (explosive) hydrogen burning or the Rapid Proton Capture Process
(rp-process) occurs in a number of astrophysical environments. Novae and X-ray
bursts are the most prominent ones, but accretion disks around black holes and
other sites are candidates as well. The expensive and often multidimensional
hydro calculations for such events require an accurate prediction of the
thermonuclear energy generation, while avoiding full nucleosynthesis network
calculations. In the present investigation we present an approximation scheme
applicable in a temperature range which covers the whole range of all presently
known astrophysical sites. It is based on the concept of slowly varying
hydrogen and helium abundances and assumes a kind of local steady flow by
requiring that all reactions entering and leaving a nucleus add up to a zero
flux. This scheme can adapt itself automatically and covers situations at low
temperatures, characterized by a steady flow of reactions, as well as high
temperature regimes where a $(p,\gamma)-(\gamma,p)$-equilibrium is established.
In addition to a gain of a factor of 15 in computational speed over a full
network calculation, and an energy generation accurate to more than 15 %, this
scheme also allows to predict correctly individual isotopic abundances. Thus,
it delivers all features of a full network at a highly reduced cost and can
easily be implemented in hydro calculations.
