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The canonical Monte-Carlo is used to study the phase transitions from thelow-temperature ordered phase to the high-temperature disordered phase in thetwo-dimensional Falicov-Kimball model with correlated hopping. As thelow-temperature ordered phase we consider the chessboard phase, the axialstriped phase and the segregated phase. It is shown that all three phasespersist 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 forthe chessboard and axial striped phase and of the second order for thesegregated phase. In addition, it is found that the critical temperature isreduced with the increasing amplitude of correlated hopping $t'$ in thechessboard phase and it is strongly enhanced by $t'$ in the axial striped andsegregated phase.

Phase transitions in the spinless Falicov-Kimball model with correlated hopping