The hybrid density functional theory was used to study the structural, vibrational, and thermodynamic properties of stable and hypothetical bulk GaTe and InTe polymorphs, as well as their monolayer counterparts. Criteria based on the vibrational frequencies have been proposed to distinguish between different monolayer structures. Heat capacity, entropy, and Helmholtz free energy have been calculated by summing the vibrational contributions over the corresponding Brillouin zone. The relative stability of the considered systems has been estimated at different temperatures using the obtained Helmholtz free energy. Both the total energy and the Helmholtz free energy calculations confirmed that a free-standing monolayer originated from the monoclinic GaTe phase is less stable than its hexagonal analogs. It was also found that the temperature increase favors monolayer formation in the case of GaTe, but prevents it in the case of InTe.