Thermal behaviour of two dimesogenic liquid crystal compounds, KI5 and KI5A, was investigated under atmospheric and hydrostatic pressure by a differential scanning calorimeter and a high-pressure DTA apparatus. The enantiotropic phase transitions of crystal - multiple mesophases - isotropic liquid for both compounds were observed under atmospheric pressure. On the other hand, only two major peaks of crystal - smectic (melting) and cholesteric - isotropic (isotropization) transitions were observed under hydrostatic pressure up to 300 MPa. Not all the multiple mesophasic transitions of the KI5 compound between the incommensurate smectic A (S-Ainc) and cholesteric (N*) phases could be detected because of their very small heat of transitions and the low sensitivity of the high-pressure DTA apparatus. A pressure-induced crystal polymorph of the KI5 compound appears at pressure above about 20 MPa and the crystal polymorph is formed preferentially under pressure above 100 MPa. The polymorph has a melting temperature higher than that of the normal crystal and it is thermodynamically stable. Enantiotropic phase transitions of crystal - S-Ainc-(TGB-N*)-I of the KI5A compound is unchanged at pressures up to 160 MPa, but double or triple peaks are observed at the crystal - S-Ainc transition under high pressure above about 180 MPa. This phenomenon is ascribed to the formation of a pressure-induced crystal polymorph and a high-pressure mesophase. The incomplete T vs. P phase diagrams of the KI5 and KI5A compounds were constructed.