  The canonical Monte-Carlo is used to study the phase transitions from the
low-temperature ordered phase to the high-temperature disordered phase in the
two-dimensional Falicov-Kimball model with correlated hopping. As the
low-temperature ordered phase we consider the chessboard phase, the axial
striped phase and the segregated phase. It is shown that all three phases
persist also at finite temperatures (up to the critical temperature $\tau_c$)
and that the phase transition at the critical point is of the first order for
the chessboard and axial striped phase and of the second order for the
segregated phase. In addition, it is found that the critical temperature is
reduced with the increasing amplitude of correlated hopping $t'$ in the
chessboard phase and it is strongly enhanced by $t'$ in the axial striped and
segregated phase.
