  Explaining the initial mass function (IMF) of stars is a long-standing
problem in astrophysics. The number of complex mechanisms involved in the
process of star cluster formation, such as turbulence, magnetic fields and
stellar feedback, make understanding and modeling the IMF a challenging task.
In this paper, we aim to assert the importance of stellar heating feedback in
the star cluster formation process and its effect on the shape of the IMF. We
use an analytical sub-grid model to implement the radiative feedback in fully
three-dimensional magnetohydrodynamical (MHD) simulations of star cluster
formation, with the ultimate objective of obtaining numerical convergence on
the IMF. We compare a set of MHD adaptive-mesh-refinement (AMR) simulations
with three different implementations of the heating of the gas: 1) a polytropic
equation of state (EOS), 2) a spherically symmetric stellar heating feedback,
and 3) our newly developed polar heating model that takes into account the
geometry of the accretion disc and the resulting shielding of stellar radiation
by dust. For each of the three heating models, we analyse the distribution of
stellar masses formed in ten molecular cloud simulations with different
realizations of the turbulence to obtain a statistically representative IMF. We
conclude that stellar heating feedback has a profound influence on the number
of stars formed and plays a crucial role in controlling the IMF. We find that
the simulations with the polar heating model achieve the best convergence on
the observed IMF.
