The accuracy of the temperature derivative of radial distribution function obtained under hypernetted chain (HNC), Kovalenko-Hirata (KH), Percus-Yevick (PY) and Verlet-modified (VM) closure approximations is examined for one-component Lennard-Jones fluid. As relevant thermodynamic quantities, constant-volume heat capacity and thermal pressure coefficient are investigated in terms of their accuracy under the above four approximations. It is found that HNC and KH closures overestimate these quantities, whereas PY closure tends to underestimate them. VM closure predicts rather accurately the quantities. A significant cancellation is observed along the integration for the above quantities under HNC and KH closures, especially at high density state. (C) 2016 Elsevier B.V. All rights reserved.