Debye temperatures and Grueneisen parameters of chain TlSe and TlInSe2 were calculated using our earlier obtained ab‐initio results on phonon band structure and existed experimental data on thermal expansion coefficient. For both compounds, the values of heat capacity at constant volume (Cv) were found to obey cubic law at temperatures less than 2 K. The Debye temperatures were determined to be 95 K and 96 K for TlSe and TInSe2, respectively. The unit cells of TlSe and TInSe2 were relaxed by minimizing Hellman‐Feynman forces and the total energy dependence on the unit cell volume was obtained. The bulk modulus (B0) values in Murnaghan and Birch‐Murnaghan equations of state were shown to be very close to each other. By using above B0 and Cv, as well as available experimental data on linear expansion, the heat capacity at constant pressure (CP) was evaluated. Comparison with experimental CP in a wide temperature range showed a good agreement for TlInSe2 and a noticeable discrepancy for TlSe at temperatures above 170 K. The calculated Grueneisen parameter of TlInSe2 showed a tendency to saturation in a region above Debye temperature. The situation with TlSe is not clear because of the ambiguous character of the available experimental data on thermal expansion. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)