  Aims. Our aim is to study deuterium burning in objects forming according to
the core accretion scenario in the hot and cold start assumption and what
minimum deuterium burning mass limit is found for these objects. We also study
how the burning process influences the structure and luminosity of the objects.
Furthermore we want to test and verify our results by comparing them to already
existing hot start simulations which did not consider, however, the formation
process.
  Methods. We present a new method to calculate deuterium burning of objects in
a self-consistently coupled model of planet formation and evolution. We discuss
which theory is used to describe the process of deuterium burning and how it
was implemented.
  Results. We find that the objects forming according to a hot start scenario
behave approximately in the same way as found in previous works of evolutionary
calculations, which did not consider the formation. However, for cold start
objects one finds that the objects expand during deuterium burning instead of
being partially stabilized against contraction. In both cases, hot and cold
start, the mass of the solid core has an influence on the minimum mass limit of
deuterium burning. The general position of the mass limit, 13 MJ, stays however
approximately the same. None of the investigated parameters was able to change
this mass limit by more than 0.8 MJ. Due to deuterium burning, the luminosity
of hot and cold start objects becomes comparable after ~ 200 Myrs.
