In canonical Monte Carlo simulations of chiral liquid crystals, generally cholesteric phases with nonequilibrium pitch were formed under periodic boundary conditions. In order to overcome system-size effects the phase diagram of chiral calamitic liquid crystals, described here by the chiral Gay-Berne fluid, was now studied by simulations in the isothermal-isobaric ensemble (NpT). In the temperature-chirality parameter plane a rich polymorphism could be proven. In the cholesteric phase the ability of the simulation box to change the dimensions during the simulations enabled the determination of the equilibrium pitch in dependence on the chirality parameter describing the strength of the chiral interaction. Additionally, in dependence on temperature first-order phase transitions characterized by phase transition enthalpy, entropy and relative volume change have been observed. On heating a cholesteric phase (N*), for the first time by computer simulation of a many-particle system based on model intermolecular interactions a temperature-driven phase transition to a blue phase could be proven, a characteristic feature of many experimental and theoretical phase diagrams of chiral liquid crystals. Additionally, on cooling a cholesteric system a phase with a helical superstructure and smectic layers formed perpendicular to the helical axis, both characteristics of a twist grain boundary (TGB) phase, has been observed. This clear evidence shows that a chiral interaction proportional to the first pseudoscalar term of the expansion in rotational invariants is able to yield the observed phase sequence TGB-like phase, cholesteric phase, blue phase, and isotropic phase in dependence on one scalar parameter given here by the temperature, only.