  The 21 cm emission of neutral hydrogen is the most promising probe of the
epoch of reionization(EoR). In the next few years, the SKA pathfinders will
provide statistical measurements of this signal. Numerical simulations
predicting these observations are necessary to optimize the design of the
instruments. The main difficulty is the computation of the spin temperature of
neutral hydrogen which depends on the gas kinetic temperature and on the level
of the local Lyman-alpha flux. A T_s >> T_cmb assumption is usual. However,
this assumption does not apply early in the reionization history, or even later
in the history as long as the sources of X-rays are too weak to heat the
intergalactic medium significantly. This work presents the first EoR numerical
simulations including, beside dynamics and ionizing continuum radiative
transfer, a self-consistent treatment of the Ly-alpha radiative transfer. This
allows us to compute the spin temperature more accurately. We use two different
box sizes, 20 Mpc/h and 100 Mpc/h, and a star source model. Using the redshift
dependence of average quantities, maps, and power spectra, we quantify the
effect of using different assumptions to compute the spin temperature and the
influence of the box size. The first effect comes from allowing for a signal in
absorption. The magnitude of this effect depends on the amount of heating by
hydrodynamic shocks and X-rays in the intergalactic medium(IGM). The second
effects comes from using the real, local, Lyman-alpha flux. This effect is
important for an average ionization fraction of less than 10%: it changes the
overall amplitude of the 21 cm signal, and adds its own fluctuations to the
power spectrum.
